title:
First principles calculations of the electronic properties of O- and
  O2-NbSe2 complexes

abstract:
  Purpose: We investigated the interaction of O and O2 on monolayer Niobium
Diselenide (NbSe2) to provide theoretical predictions about the electronic
properties of the complexes using First principles calculations in Quantum
Espresso 6.7. As known, considering impurities in pristine nanomaterials like
NbSe2 is very important as it can alter some of its properties.
  Method: In this paper, we performed some topological analyses on the
electronic densities and electronic structures calculations to O- and O2-NbSe2
complexes. Charge Density Difference (CDD) and Bader charge analysis reveal
that O and O2 acted as oxidizing agents and accumulated electronic charges from
the NbSe2.
  Results: The electronic properties calculations of the complexes showed that
the metallic behavior of NbSe2 is preserved after O and O2 adsorption.
Calculations of the net charge transfer revealed that the atomic and molecular
oxygen has accumulated electronic charges while the NbSe2 has depleted
electronic charges. These results showed the possibility of tailoring the
electronic properties of NbSe2.
  Conclusion: The interaction of O and O2 with the monolayer NbSe2 caused
charge redistributions while maintaining the metallicity of the NbSe2. In all
circumstances, the results are consistent with the established works which show
the possibility of modifying the electronic properties of NbSe2 that could open
some potential applications in nanotechnology and other nanoelectronics-related
devices.


title:
Escaping Saddle Points with Bias-Variance Reduced Local Perturbed SGD
  for Communication Efficient Nonconvex Distributed Learning

abstract:
  In recent centralized nonconvex distributed learning and federated learning,
local methods are one of the promising approaches to reduce communication time.
However, existing work has mainly focused on studying first-order optimality
guarantees. On the other side, second-order optimality guaranteed algorithms
have been extensively studied in the non-distributed optimization literature.
In this paper, we study a new local algorithm called Bias-Variance Reduced
Local Perturbed SGD (BVR-L-PSGD), that combines the existing bias-variance
reduced gradient estimator with parameter perturbation to find second-order
optimal points in centralized nonconvex distributed optimization. BVR-L-PSGD
enjoys second-order optimality with nearly the same communication complexity as
the best known one of BVR-L-SGD to find first-order optimality. Particularly,
the communication complexity is better than non-local methods when the local
datasets heterogeneity is smaller than the smoothness of the local loss. In an
extreme case, the communication complexity approaches to $\widetilde \Theta(1)$
when the local datasets heterogeneity goes to zero.


title: EREBA: Black-box Energy Testing of Adaptive Neural Networks

abstract:
  Recently, various Deep Neural Network (DNN) models have been proposed for
environments like embedded systems with stringent energy constraints. The
fundamental problem of determining the robustness of a DNN with respect to its
energy consumption (energy robustness) is relatively unexplored compared to
accuracy-based robustness. This work investigates the energy robustness of
Adaptive Neural Networks (AdNNs), a type of energy-saving DNNs proposed for
many energy-sensitive domains and have recently gained traction. We propose
EREBA, the first black-box testing method for determining the energy robustness
of an AdNN. EREBA explores and infers the relationship between inputs and the
energy consumption of AdNNs to generate energy surging samples. Extensive
implementation and evaluation using three state-of-the-art AdNNs demonstrate
that test inputs generated by EREBA could degrade the performance of the system
substantially. The test inputs generated by EREBA can increase the energy
consumption of AdNNs by 2,000% compared to the original inputs. Our results
also show that test inputs generated via EREBA are valuable in detecting energy
surging inputs.


title: Online V2X Scheduling for Raw-Level Cooperative Perception

abstract:
  Cooperative perception of connected vehicles comes to the rescue when the
field of view restricts stand-alone intelligence. While raw-level cooperative
perception preserves most information to guarantee accuracy, it is demanding in
communication bandwidth and computation power. Therefore, it is important to
schedule the most beneficial vehicle to share its sensor in terms of
supplementary view and stable network connection. In this paper, we present a
model of raw-level cooperative perception and formulate the energy minimization
problem of sensor sharing scheduling as a variant of the Multi-Armed Bandit
(MAB) problem. Specifically, volatility of the neighboring vehicles,
heterogeneity of V2X channels, and the time-varying traffic context are taken
into consideration. Then we propose an online learning-based algorithm with
logarithmic performance loss, achieving a decent trade-off between exploration
and exploitation. Simulation results under different scenarios indicate that
the proposed algorithm quickly learns to schedule the optimal cooperative
vehicle and saves more energy as compared to baseline algorithms.


title:
From the String Landscape to the Mathematical Landscape: a
  Machine-Learning Outlook

abstract:
  We review the recent programme of using machine-learning to explore the
landscape of mathematical problems. With this paradigm as a model for human
intuition - complementary to and in contrast with the more formalistic approach
of automated theorem proving - we highlight some experiments on how AI helps
with conjecture formulation, pattern recognition and computation.


title: A note on the width of sparse random graphs

abstract:
  In this note, we consider the width of a supercritical random graph according
to some commonly studied width measures. We give short, direct proofs of
results of Lee, Lee and Oum, and of Perarnau and Serra, on the rank- and
tree-width of the random graph $G(n,p)$ when $p= \frac{1+\epsilon}{n}$ for
$\epsilon > 0$ constant. Our proofs avoid the use, as a black box, of a result
of Benjamini, Kozma and Wormald on the expansion properties of the giant
component in this regime, and so as a further benefit we obtain explicit bounds
on the dependence of these results on $\epsilon$. Finally, we also consider the
width of the random graph in the weakly supercritical regime, where $\epsilon =
o(1)$ and $\epsilon^3n \to \infty$. In this regime, we determine, up to a
constant multiplicative factor, the rank- and tree-width of $G(n,p)$ as a
function of $n$ and $\epsilon$.


title: NeuVV: Neural Volumetric Videos with Immersive Rendering and Editing

abstract:
  Some of the most exciting experiences that Metaverse promises to offer, for
instance, live interactions with virtual characters in virtual environments,
require real-time photo-realistic rendering. 3D reconstruction approaches to
rendering, active or passive, still require extensive cleanup work to fix the
meshes or point clouds. In this paper, we present a neural volumography
technique called neural volumetric video or NeuVV to support immersive,
interactive, and spatial-temporal rendering of volumetric video contents with
photo-realism and in real-time. The core of NeuVV is to efficiently encode a
dynamic neural radiance field (NeRF) into renderable and editable primitives.
We introduce two types of factorization schemes: a hyper-spherical harmonics
(HH) decomposition for modeling smooth color variations over space and time and
a learnable basis representation for modeling abrupt density and color changes
caused by motion. NeuVV factorization can be integrated into a Video Octree
(VOctree) analogous to PlenOctree to significantly accelerate training while
reducing memory overhead. Real-time NeuVV rendering further enables a class of
immersive content editing tools. Specifically, NeuVV treats each VOctree as a
primitive and implements volume-based depth ordering and alpha blending to
realize spatial-temporal compositions for content re-purposing. For example, we
demonstrate positioning varied manifestations of the same performance at
different 3D locations with different timing, adjusting color/texture of the
performer's clothing, casting spotlight shadows and synthesizing distance
falloff lighting, etc, all at an interactive speed. We further develop a hybrid
neural-rasterization rendering framework to support consumer-level VR headsets
so that the aforementioned volumetric video viewing and editing, for the first
time, can be conducted immersively in virtual 3D space.


title: Spectral gap characterizations of property (T) for II$_1$ factors

abstract:
  For II$_1$ factors, we show that property (T) is equivalent to weak spectral
gap in any inclusion into a larger tracial von Neumann algebra. We also show
that not having non-zero almost central vectors in weakly mixing bimodules
characterizes property (T) for II$_1$ factors, which allows us to obtain a
stronger characterization of property (T) where only weak spectral gap in any
irreducible inclusion is required.


title: Quantum Duality Principle for quantum continuous Kac-Moody algebras

abstract:
  For the quantized universal enveloping algebra U_h(g_X) associated with a
continuous Kac-Moody algebra g_X as in [A. Appel, F. Sala, "Quantization of
continuum Kac-Moody algebras", Pure Appl. Math. Q. 16 (2020), no. 3, 439-493],
we prove that a suitable formulation of the Quantum Duality Principle holds
true, both in a "formal" version - i.e., applying to the original definition of
U_h(g_X) as a formal QUEA over the algebra of formal series in h - and in a
"polynomial" one - i.e., for a suitable polynomial form of U_h(g_X) over the
algebra of Laurent polynomials in q. In both cases, the QDP states that a
suitable subalgebra of the given quantization of the Lie bialgebra g_X is in
fact a suitable quantization (in formal or in polynomial sense) of a connected
Poisson group G^*_X dual to g_X .


title:
TATTOOED: A Robust Deep Neural Network Watermarking Scheme based on
  Spread-Spectrum Channel Coding

abstract:
  The proliferation of deep learning applications in several areas has led to
the rapid adoption of such solutions from an ever-growing number of
institutions and companies. These entities' deep neural network (DNN) models
are often trained on proprietary data. They require powerful computational
resources, with the resulting DNN models being incorporated in the company's
work pipeline or provided as a service. Being trained on proprietary
information, these models provide a competitive edge for the owner company. At
the same time, these models can be attractive to competitors (or malicious
entities), which can employ state-of-the-art security attacks to obtain and use
these models for their benefit. As these attacks are hard to prevent, it
becomes imperative to have mechanisms that enable an affected entity to verify
the ownership of its DNN with high confidence. This paper presents TATTOOED, a
robust and efficient DNN watermarking technique based on spread-spectrum
channel coding. TATTOOED has a negligible effect on the performance of the DNN
model and is robust against several state-of-the-art mechanisms used to remove
watermarks from DNNs. Our results show that TATTOOED is robust to such removal
techniques even in extreme scenarios. For example, if the removal techniques
such as fine-tuning and parameter pruning change as much as 99% of the model
parameters, the TATTOOED watermark is still present in full in the DNN model
and ensures ownership verification.


title: Geometry of static $w=-1/5$ perfect fluid spheres in general relativity

abstract:
  We discuss the physical features of two recent classes of analytical
solutions of the Einstein equations sourced by an exotic perfect fluid with
equation of state $ P=-\rho/5$. These geometries depend on up to four
parameters and are static and spherically symmetric. They describe compact
spaces with naked central singularities.


title: Type V singularities in non-standard cosmological backgrounds

abstract:
  Interest in cosmological singularities has remarkably grown in recent times,
particularly on future singularities with the discovery of late-time
acceleration of the universe and dark energy. Recent work has seen a proper
classification of such singularities into strong and weak based on their
strength, with weak singularities being the likes of sudden, w and big freeze
singularities and strong singularities like the big rip. While there has been
an expansive literature which has discussed the occurrence of Type I-IV in many
non-standard cosmologies, w-singularities have not yet been explored in exotic
cosmological settings. So in this work we pursue the same and discuss the
status quo of w-singularities in a variety of non-standard cosmologies. We
consider the RS-II Braneworld cosmology, an F(R) gravity cosmology which gives
viable late time acceleration. We also consider cosmologies due to modified
area-entropy relations, generalized uncertainty principles, holographic
renormalization and Chern-Simons gravity( all of which can be coincidentally
described by the same form of the modified Friedmann equation). We show that
w-singularities will occur in exactly the same conditions in all these vividly
different cosmological settings as they do in the usual general relativistic
cosmology if one considers a power series expansion ansatz for the scale
factor. We also show that if one considers an exponential form of the scale
factor then while Type V singularities in the RS-II Braneworld and Chern-Simons
cosmologies occur in the same conditions as in the standard cosmology case,
there is a significant difference in the conditions when one considers the f(R)
gravity case. These results are surprising overall, as one would usually not
expect cosmological singularities to occur in almost the same conditions in
non-standard cosmologies as they do in the usual standard cosmology.


title:
Modeling Stellar Oscillations and Granulation in Radial Velocity Time
  Series: A Fourier-based Method

abstract:
  Tens of thousands of solar-like oscillating stars have been observed by space
missions. Their photometric variability in the Fourier domain can be
parameterized by a sum of two super-Lorentizian functions for granulation and a
Gaussian-shaped power excess for oscillation. The photometric
granulation/oscillation parameters scale with stellar parameters and they can
also make predictions for corresponding parameters in radial velocity
measurements. Based on scaling relations, we simulate realistic radial velocity
time series and examine how the root-mean-square scatter of radial velocity
measurements varies with stellar parameters and different observation
strategies such as the length of integration time and gaps in the time series.
Using stars with extensive spectroscopic observations from the spectrographs
(SONG and HARPS), we measure the granulation amplitude and timescale from the
power spectrum of the radial velocity time series. We compare these
measurements with literature values based on Kepler photometry. We find that
the granulation amplitude in radial velocity can be well predicted from the
photometry and scaling relations. Both granulation timescales in radial
velocity agree with those predicted from photometry for giants and sub-giants.
However, for main-sequence stars, only one granulation timescale in radial
velocity is in agreement with the photometric-based values, while the other
timescale generally lies at lower frequencies compared to the result of
photometry. In conclusion, we show the photometric scaling relations from
Kepler photometry and the scaling relationship to Doppler observations can be
very useful for predicting the photometric and radial velocity stellar
variabilities due to stellar granulation and oscillation.


title:
A Review of Deep Learning-based Approaches for Deepfake Content
  Detection

abstract:
  The fast-spreading information over the internet is essential to support the
rapid supply of numerous public utility services and entertainment to users.
Social networks and online media paved the way for modern,
timely-communication-fashion and convenient access to all types of information.
However, it also provides new chances for ill use of the massive amount of
available data, such as spreading fake content to manipulate public opinion.
Detection of counterfeit content has raised attention in the last few years for
the advances in deepfake generation. The rapid growth of machine learning
techniques, particularly deep learning, can predict fake content in several
application domains, including fake image and video manipulation. This paper
presents a comprehensive review of recent studies for deepfake content
detection using deep learning-based approaches. We aim to broaden the
state-of-the-art research by systematically reviewing the different categories
of fake content detection. Furthermore, we report the advantages and drawbacks
of the examined works and future directions towards the issues and shortcomings
still unsolved on deepfake detection.


title:
Improving Fraud Detection via Hierarchical Attention-based Graph Neural
  Network

abstract:
  Graph neural networks (GNN) have emerged as a powerful tool for fraud
detection tasks, where fraudulent nodes are identified by aggregating neighbor
information via different relations. To get around such detection, crafty
fraudsters resort to camouflage via connecting to legitimate users (i.e.,
relation camouflage) or providing seemingly legitimate feedbacks (i.e., feature
camouflage). A wide-spread solution reinforces the GNN aggregation process with
neighbor selectors according to original node features. This method may carry
limitations when identifying fraudsters not only with the relation camouflage,
but with the feature camouflage making them hard to distinguish from their
legitimate neighbors. In this paper, we propose a Hierarchical Attention-based
Graph Neural Network (HA-GNN) for fraud detection, which incorporates weighted
adjacency matrices across different relations against camouflage. This is
motivated in the Relational Density Theory and is exploited for forming a
hierarchical attention-based graph neural network. Specifically, we design a
relation attention module to reflect the tie strength between two nodes, while
a neighborhood attention module to capture the long-range structural affinity
associated with the graph. We generate node embeddings by aggregating
information from local/long-range structures and original node features.
Experiments on three real-world datasets demonstrate the effectiveness of our
model over the state-of-the-arts.


title:
Using embedding theorems to account for the extreme properties of
  traversable wormholes

abstract:
  Embedding theorems, which have a long history in the general theory of
relativity, are used in this paper to account for two of the most troubling
aspects of Morris-Thorne wormholes, (1) the origin of exotic matter and the
amount needed to sustain a wormhole, and (2) the enormous radial tension that
is characteristic of wormholes with moderately-sized throats. Attributing the
latter to exotic matter ignores the fact that exotic matter was introduced for
a completely different reason and is usually present in only small quantities.


title: Kirigami, the Verifiable Art of Network Cutting

abstract:
  We introduce a modular verification approach to network control plane
verification, where we cut a network into smaller fragments to improve the
scalability of SMT solving. Users provide an annotated cut which describes how
to generate these fragments from the monolithic network, and we verify each
fragment independently, using the annotations to define assumptions and
guarantees over fragments akin to assume-guarantee reasoning. We prove this
modular network verification procedure is sound and complete with respect to
verification over the monolithic network. We implement this procedure as
Kirigami, an extension of NV - a network verification language and tool - and
evaluate it on industrial topologies with synthesized policies. We observe a
2-8x improvement in end-to-end NV verification time, with SMT solve time
improving by up to 6 orders of magnitude.


title:
The Eigenvalue Problem of Nonlinear Schr\"odinger Equation at Dirac
  Points of Honeycomb Lattice

abstract:
  We give a rigorous deduction of the eigenvalue problem of the nonlinear
Schr\"odinger equation (NLS) at Dirac Points for potential of honeycomb lattice
symmetry. Based on a bootstrap method, we observe the bifurcation of the
eigenfunctions into eight distinct modes from the two-dimensional degenerated
eigenspace of the regressive linear Schr\"odinger equation. We give the
existence, the way of construction, uniqueness in $H^2$ space and the
$C^\infty$ continuity of these eigenfunctions.

categories: math.AP cond-mat.mtrl-sci math-ph math.MP physics.optics quant-ph


title:
Finite-size Kosterlitz-Thouless transition in a ferromagnetic ultrathin
  film with fourfold anisotropy: Determination of the exchange coupling, vortex
  density, anisotropy and magnetic susceptibility

abstract:
  The renormalization group equations describing a finite 2DXY system with
fourfold anisotropy are solved in two steps, in order to study the magnetic
transition to paramagnetism in an ultrathin film. First, the equations are
linearized near the critical coupling $K=J/k_BT=2/\pi$. This allows integration
constants to be evaluated at the fixed point, and the tuning of the constants
to represent a ferromagnetic ultrathin film. An exact solution of the
linearized equations confirms that a finite-size Kosterlitz-Thouless (KT)
transition can occur in the presence of fourfold anisotropy, but the solution
is not quantitatively reliable across the temperature range of the finite-size
transition. In the second approach, the fourfold anisotropy is treated as a
perturbation. The perturbative treatment provides a quantitative determination
of the renormalized exchange coupling, vortex density, and anisotropy
throughout the transition. In particular, the coupling has a point of
inflection where vortex-antivortex pairs unbind (as opposed to a "universal
jump"), and goes to zero asymptotically in the paramagnetic state. These
results are used to calculate the magnetic susceptibility as the system moves
from one dominated by spin waves to one dominated by a free vortex gas. The
presence of anisotropy makes it necessary to include both the susceptibility
$\chi_{||}$ due to fluctuations of the magnitude of the magnetization, and
$\chi_\perp$ due to angular fluctuations of the magnetization about an easy
axis. Comparison to recent measurements of the magnetic susceptibility of
ultrathin Fe/W(001) films suggest that a detailed quantitative analysis of the
measurements can provide information on vortex formation, the disappearance of
anisotropy, and dissipative processes in the finite-size KT transition of a
real system.


title:
A New Window to Tidal Asteroseismology: Non-linearly Excited Stellar
  Eigenmodes and the Period Spacing Pattern in KOI-54

abstract:
  We revisit the Tidally Excited Oscillations (TEOs) in the A-type,
main-sequence, eccentric binary KOI-54 (KIC 8112039), the prototype of
heartbeat stars. Although the linear tidal response of the star is a series of
orbital-harmonic frequencies which are not stellar eigenfrequencies, we show
that the non-linearly excited non-orbital-harmonic TEOs are eigenmodes. By
carefully choosing the modes having the same $l$ and $m$ which satisfy the
mode-coupling selection rules, a period spacing pattern of quadrupole gravity
modes ($\Delta P \approx 2520$ sec) can be discerned in the Fourier spectrum
and its echelle diagram. The inferred period spacing value agrees remarkably
well with the theoretical $l=2,m=0$ g modes from a star with measured mass,
radius and effective temperature. We also find that the two largest-amplitude
TEOs at $N=90, 91$ harmonics are very close to resonance with $l=2,m=0$
eigenmodes, and likely come from different stars. They can essentially be
regarded as eigenfrequencies to infer the stellar parameters.


title: Overdamped Lattice Dynamics of Sedimenting Active Cosserat Crystals

abstract:
  Micropolar active matter requires for its kinematic description both
positional and orientational degrees of freedom. Activity generates dynamic
coupling between these kinematic variables that are absent in micropolar
passive matter, such as the oriented crystals first studied by the Cosserat
brothers. Here we study the effect of uniaxial activity on the dynamics of an
initially crystalline state of spheroidal colloids sedimenting slowly in a
viscous fluid remote from confining boundaries. Despite frictional overdamping
by the fluid, the crystalline lattice admits traveling waves of position and
orientation. At long wavelengths these obey a vector wave equation with Lam\'e
constants determined by the activity. We find that at least one polarization
mode of these waves is always unstable, leading to the melting of the crystal.
These results are elucidated by identifying an odd-dimensional Poisson
structure consisting of a Hamiltonian and an associated Casimir invariant,
where linear combinations of position and orientation are identified as
conjugate variables. Our results suggest that Poisson structures may exist
generally for active particles in slow viscous flow and thereby allow
equilibrium arguments to be applied in the presence of these dissipative
systems.


title: Representations of Munn algebras and related semigroups

abstract:
  We establish representation types (finite, tame or wild) of finite
dimensional Munn algebras with semisimple bases. As an application, we
  establish representation types of finite 0-simple semigroups and their
mutually annihilating unions.


title:
Semi-supervised Medical Image Segmentation via Geometry-aware
  Consistency Training

abstract:
  The performance of supervised deep learning methods for medical image
segmentation is often limited by the scarcity of labeled data. As a promising
research direction, semi-supervised learning addresses this dilemma by
leveraging unlabeled data information to assist the learning process. In this
paper, a novel geometry-aware semi-supervised learning framework is proposed
for medical image segmentation, which is a consistency-based method.
Considering that the hard-to-segment regions are mainly located around the
object boundary, we introduce an auxiliary prediction task to learn the global
geometric information. Based on the geometric constraint, the ambiguous
boundary regions are emphasized through an exponentially weighted strategy for
the model training to better exploit both labeled and unlabeled data. In
addition, a dual-view network is designed to perform segmentation from
different perspectives and reduce the prediction uncertainty. The proposed
method is evaluated on the public left atrium benchmark dataset and improves
fully supervised method by 8.7% in Dice with 10% labeled images, while 4.3%
with 20% labeled images. Meanwhile, our framework outperforms six
state-of-the-art semi-supervised segmentation methods.


title: On Federated Learning with Energy Harvesting Clients

abstract:
  Catering to the proliferation of Internet of Things devices and distributed
machine learning at the edge, we propose an energy harvesting federated
learning (EHFL) framework in this paper. The introduction of EH implies that a
client's availability to participate in any FL round cannot be guaranteed,
which complicates the theoretical analysis. We derive novel convergence bounds
that capture the impact of time-varying device availabilities due to the random
EH characteristics of the participating clients, for both parallel and local
stochastic gradient descent (SGD) with non-convex loss functions. The results
suggest that having a uniform client scheduling that maximizes the minimum
number of clients throughout the FL process is desirable, which is further
corroborated by the numerical experiments using a real-world FL task and a
state-of-the-art EH scheduler.


title:
A Fully Decentralized Tuning-free Inexact Projection Method for P2P
  Energy Trading

abstract:
  Agent-based solutions lend themselves well to address privacy concerns and
the computational scalability needs of future distributed electric grids and
end-use energy exchanges. Decentralized decision-making methods are the key to
enabling peer-to-peer energy trading between electricity prosumers. However,
the performance of existing decentralized decision-making algorithms highly
depends on the algorithmic design and hyperparameter tunings, limiting
applicability. This paper aims to address this gap by proposing a decentralized
inexact projection method that does not rely on parameter tuning or central
coordination to achieve the optimal solution for Peer-to-Peer (P2P) energy
trading problems. The proposed algorithm does not require parameter
readjustments, and once tuned, it converges for a wide range of P2P setups.
Moreover, each prosumer only needs to share limited information (i.e., updated
coupled variable) with neighboring prosumers. The IEEE 13 bus test system is
used to showcase our proposed method's robustness and privacy advantages.


title: Nonlinear Meissner effect in Nb3Sn coplanar resonators

abstract:
  We investigated the nonlinear Meissner effect (NLME) in Nb$_3$Sn thin film
coplanar resonators by measuring the resonance frequency as a function of a
parallel magnetic field at different temperatures. We used low rf power probing
in films thinner than the London penetration depth $\lambda(B)$ to
significantly increase the field onset of vortex penetration and measure the
NLME under equilibrium conditions. Contrary to the conventional quadratic
increase of $\lambda(B)$ with $B$ expected in s-wave superconductors, we
observed a nearly linear increase of the penetration depth with $B$. We
concluded that this behavior of $\lambda(B)$ is due to weak linked grain
boundaries in our polycrystalline Nb$_3$Sn films, which can mimic the NLME
expected in a clean d-wave superconductor.


title: Mitigating the Effects of Ransomware Attacks on Healthcare Systems

abstract:
  Healthcare information systems deal with a large amount of Personally
Identifiable Information related to patients like dates of birth and social
security numbers, patients health information and history, and financial
information like credit card details and bank accounts. Most healthcare
institutions purchase information systems from commercial vendors and have
minimal inhouse expertise required to maintain these systems. Most institutions
lack the expertise required to research evolving threats and maintain a tough
security posture. We propose a risk transference based system architecture that
moves sensitive data outside the system boundary, into data stores that are
managed with stringent and efficient security protocols.


title: Breast Cancer Detection using Histopathological Images

abstract:
  Cancer is one of the most common and fatal diseases in the world. Breast
cancer affects one in every eight women and one in every eight hundred men.
Hence, our prime target should be early detection of cancer because the early
detection of cancer can be helpful to cure cancer effectively. Therefore, we
propose a saliency detection system with the help of advanced deep learning
techniques, such that the machine will be taught to emulate actions of
pathologists for localization of diagnostically pertinent regions. We study
identification of five diagnostic categories of breast cancer by training a CNN
(VGG16, ResNet architecture). We have used BreakHis dataset to train our model.
We focus on both detection and classification of cancerous regions in
histopathology images. The diagnostically relevant regions are salient. The
detection system will be available as an open source web application which can
be used by pathologists and medical institutions.


title: On quasi-isospectral potentials

abstract:
  In the first part of this article we present some known results about
isospectral potentials on compact manifolds and on finite intervals. Then we
look at a weaker notion called quasi-isospectrality and deduce some properties
of quasi-isospectral potentials.


title:
An efficient implementation of graph-based invariant set algorithm for
  constrained nonlinear dynamical systems

abstract:
  The graph-based invariant set (GIS) algorithm is a promising set-based
technique for computing the largest (with respect to inclusion) control
invariant set of general discrete-time nonlinear dynamical systems. However,
like other invariant set algorithms for nonlinear systems, the GIS algorithm
may require a lot of resources when computing the control invariant set. This
limits its applicability to higher dimensional systems. In this work, we
present an improved and efficient implementation of the GIS algorithm for
general discrete-time controlled nonlinear systems. We first identify the
bottlenecks through extensive analysis, and then provide remedial procedures to
improve the implementation of the GIS algorithm. Specifically, we developed an
adaptive subdivision scheme using a supervised machine learning-based algorithm
to reduce the cell growth rate and parallelize the graph construction step. We
extensively demonstrate the performance of the improved GIS algorithm using a
numerical example and compare the result to that of the standard GIS algorithm.
The results show that the adaptive subdivision and the parallelization improved
the speed of the algorithm by about 8x and 3x respectively, that of the
standard GIS algorithm.


title: Conservation laws in gauge gravity theory

abstract:
  We analyse the conservation laws in the gauge gravity theory which are
derived for the general class of gravitational models with the action invariant
under the local Poincare and the diffeomorphism group. The consistent
Noether-Lagrange formalism is developed, revealing the important role of the
auxiliary Goldstone and Stueckelberg fields, with the help of which we
construct the composite gauge fields that have a clear geometrical and physical
meaning.


title: Lagrangian time-analyticity for the Euler equations in a Sobolev domain

abstract:
  Assuming only Sobolev regularity of the domain, we prove time-analyticity of
Lagrangian trajectories for solutions of the Euler equations.


title:
Gradient-Free Optimization for Non-Smooth Minimax Problems with Maximum
  Value of Adversarial Noise

abstract:
  In this paper, we study gradient-free methods for non-smooth convex-concave
minimax problems. We assume that a black-box gradient-free oracle returns an
inexact function value corrupted by adversarial noise. We prove that a
zeroth-order version of the mirror descent method with inexact oracle is
optimal in terms of the oracle calls complexity and the maximum value of
adversarial noise.


title: Trinomials and Deterministic Complexity Limits for Real Solving

abstract:
  Consider a univariate polynomial f in Z[x] with degree d, exactly t monomial
terms, and coefficients in {-H,...,H}. Solving f over the reals, R, in
polynomial-time can be defined as counting the exact number of real roots of f
and then finding (for each such root z) an approximation w of logarithmic
height (log(dH))^{O(1)} such that the Newton iterates of w have error decaying
at a rate of O((1/2)^{2^i}). Solving efficiently in this sense, using
(log(dH))^{O(1)} deterministic bit operations, is arguably the most honest
formulation of solving a polynomial equation over R in time polynomial in the
input size. Unfortunately, deterministic algorithms this fast are known only
for t=2, unknown for t=3, and provably impossible for t=4. (One can of course
resort to older techniques with complexity (d\log H)^{O(1)} for t>=4.)
  We give evidence that polynomial-time real-solving in the strong sense above
is possible for t=3: We give a polynomial-time algorithm employing
A-hypergeometric series that works for all but a fraction of 1/Omega(log(dH))
of the input f. We also show an equivalence between fast trinomial solving and
sign evaluation at rational points of small height. As a consequence, we show
that for "most" trinomials f, we can compute the sign of f at a rational point
r in time polynomial in log(dH) and the logarithmic height of r. (This was
known only for binomials before.) We also mention a related family of
polynomial systems that should admit a similar speed-up for solving.


title:
Fast and accurate domain decomposition methods for reduced fracture
  models with nonconforming time grids

abstract:
  This paper is concerned with the numerical solution of compressible fluid
flow in a fractured porous medium. The fracture represents a fast pathway
(i.e., with high permeability) and is modeled as a hypersurface embedded in the
porous medium. We aim to develop fast-convergent and accurate global-in-time
domain decomposition (DD) methods for such a reduced fracture model, in which
smaller time step sizes in the fracture can be coupled with larger time step
sizes in the subdomains. Using the pressure continuity equation and the
tangential PDEs in the fracture-interface as transmission conditions, three
different DD formulations are derived; each method leads to a space-time
interface problem which is solved iteratively and globally in time. Efficient
preconditioners are designed to accelerate the convergence of the iterative
methods while preserving the accuracy in time with nonconforming grids.
Numerical results for two-dimensional problems with non-immersed and partially
immersed fractures are presented to show the improved performance of the
proposed methods.


title:
Depth profiles and the geometric exploration of random objects through
  optimal transport

abstract:
  We propose new tools for the geometric exploration of data objects taking
values in a general separable metric space $(\Omega, d)$. Given a probability
measure on $\Omega$, we introduce depth profiles, where the depth profile of an
element $\omega\in\Omega$ refers to the distribution of the distances between
$\omega$ and the other elements of $\Omega$. Depth profiles can be harnessed to
define transport ranks, which capture the centrality of each element in
$\Omega$ with respect to the entire data cloud based on the optimal transport
maps between the depth profiles. We study the properties of transport ranks and
show that they provide an effective device for detecting and visualizing
patterns in samples of random objects. Specifically, we study estimates of
depth profiles and transport ranks based on samples of random objects and
establish the convergence of the empirical estimates to the population targets
using empirical process theory. We demonstrate the usefulness of depth profiles
and associated transport ranks and visualizations for distributional data
through a sample of age-at-death distributions for various countries, for
compositional data through energy usage for U.S. states and for network data
through New York taxi trips.


title: Knots, Braids, and Knot Invariants

abstract:
  In this report, I will start by first giving a brief introduction on knots to
build some intuition before beginning the more rigorous review in the
Literature Review section. There, I will define knot equivalence, the Jones
polynomial invariant, braid groups, Hecke algebras, and the HOMFLY polynomial
invariant. Next, I will cover some of my independent research regarding the
computation of a general formula for the HOMFLY polynomial of the closure of
looped coxeter braids. Lastly, I will loosely discuss how this research
connects to future research regarding the universal trace in the Plan for
Future Work section.


title: Remarks on the $L^p$ convergence of Bessel--Fourier series on the disc

abstract:
  The $L^p$ convergence of eigenfunction expansions for the Laplacian on planar
domains is largely unknown for $p\neq 2$. After discussing the classical
Fourier series on the 2-torus, we move onto the disc, whose eigenfunctions are
explicitly computable as products of trigonometric and Bessel functions. We
summarise a result of Balodis and C\'ordoba (1999) regarding the $L^p$
convergence of the Bessel--Fourier series in the mixed norm space
$L^p_{\mathrm{rad}}(L^2_{\mathrm{ang}})$ on the disk for the range
$\tfrac{4}{3}<p<4$. We then describe how to modify their result to obtain
$L^p(\mathbb{D}, r\,\mathrm{d}r\,\mathrm{d}t)$ norm convergence in the subspace
$L^p_{\mathrm{rad}}(L^q_{\mathrm{ang}})$($\tfrac{1}{p}+\tfrac{1}{q}=1$) for the
restricted range ${2\leq p < 4}$.


title: Hyper-entangling mesoscopic bound states

abstract:
  We predict hyper-entanglement generation during binary scattering of
mesoscopic bound states, solitary waves in Bose-Einstein condensates containing
thousands of identical Bosons. This requires collisions in elongated, cigar
shaped traps, in which the residual presence of transverse dimensions gives
rise to effective interactions that are cubic and quintic in the particle
density, in a dimensionally reduced description. Under these integrability
breaking conditions, we show that the post-collision state of an initially
fragmented soliton pair can be hyper-entangled in spatial degrees of freedom
and atom number within solitons, for realistic parameters. For this, we model
collisions of quantum solitons in the quintic model beyond the mean-field,
using the truncated Wigner approximation.


title: Adaptive truncation of infinite sums: applications to Statistics

abstract:
  It is often the case in Statistics that one needs to compute sums of infinite
series, especially in marginalising over discrete latent variables. This has
become more relevant with the popularization of gradient-based techniques (e.g.
Hamiltonian Monte Carlo) in the Bayesian inference context, for which discrete
latent variables are hard or impossible to deal with. For many commonly used
infinite series, custom algorithms have been developed which exploit specific
features of each problem. General techniques, suitable for a large class of
problems with limited input from the user are less established. We employ basic
results from the theory of infinite series to investigate general,
problem-agnostic algorithms to truncate infinite sums within an arbitrary
tolerance $\varepsilon > 0$ and provide robust computational implementations
with provable guarantees. We compare three tentative solutions to estimating
the infinite sum of interest: (i) a "naive" approach that sums terms until the
terms are below the threshold $\varepsilon$; (ii) a `bounding pair' strategy
based on trapping the true value between two partial sums; and (iii) a `batch'
strategy that computes the partial sums in regular intervals and stops when
their difference is less than $\varepsilon$. We show under which conditions
each strategy guarantees the truncated sum is within the required tolerance and
compare the error achieved by each approach, as well as the number of function
evaluations necessary for each one. A detailed discussion of numerical issues
in practical implementations is also provided. The paper provides some
theoretical discussion of a variety of statistical applications, including raw
and factorial moments and count models with observation error. Finally,
detailed illustrations in the form noisy MCMC for Bayesian inference and
maximum marginal likelihood estimation are presented.


title:
Linearized Field Equations and Extra Force in $f(R,{\bf T}^{(n)})$
  Extended Gravity

abstract:
  We consider an extended theory of gravity with Lagrangian $\mathcal{L} =
f(R,{\bf T}^{(n)})$, with ${\bf T}^{(n)}$ being a $2n$-th order invariant made
of contractions of the energy-momentum tensor. When $n=1$ this theory reduces
to $f(R,T)$ gravity, where $T$ accounts for the trace of the energy-momentum
tensor. We study the gravitational wave polarization modes, from which it
results that when the matter Lagrangian contains dynamical scalar fields
minimally coupled to the geometry, further polarization modes arise with
respect to General Relativity. Finally we show that the motion for test
particles is non-geodesic and we explicitly obtain the extra-force.


title:
How accurate models of human behavior are needed for human-robot
  interaction? For automated driving?

abstract:
  There are many examples of cases where access to improved models of human
behavior and cognition has allowed creation of robots which can better interact
with humans, and not least in road vehicle automation this is a rapidly growing
area of research. Human-robot interaction (HRI) therefore provides an important
applied setting for human behavior modeling - but given the vast complexity of
human behavior, how complete and accurate do these models need to be? Here, we
outline some possible ways of thinking about this problem, starting from the
suggestion that modelers need to keep the right end goal in sight: A successful
human-robot interaction, in terms of safety, performance, and human
satisfaction. Efforts toward model completeness and accuracy should be focused
on those aspects of human behavior to which interaction success is most
sensitive. We emphasise that identifying which those aspects are is a difficult
scientific objective in its own right, distinct for each given HRI context. We
propose and exemplify an approach to formulating a priori hypotheses on this
matter, in cases where robots are to be involved in interactions which
currently take place between humans, such as in automated driving. Our
perspective also highlights some possible risks of overreliance on
machine-learned models of human behavior in HRI, and how to mitigate against
those risks.


title:
Electromagnetic total-f algorithm for gyrokinetic particle-in-cell
  simulations of boundary plasma in XGC

abstract:
  The simplified delta-f mixed-variable/pull-back electromagnetic simulation
algorithm implemented in XGC for core plasma simulations by M. Cole et al.
[Phys. Plasmas 28, 034501 (2021)] has been generalized to a total-f
electromagnetic algorithm that can include, for the first time, the boundary
plasma in diverted magnetic geometry with neutral particle recycling,
turbulence and neoclassical physics. The delta-f mixed-variable/pull-back
electromagnetic is based on the pioneering work by Kleiber and Mischenko et al.
[R. Kleiber et al., Phys. Plasmas 23, 032501 (2016); A. Mishchenko et al.,
Comput. Phys. Commun. 238, 194 (2019)]. An electromagnetic demonstration
simulation is performed in a DIII-D-like, H-mode boundary plasma, including a
corresponding comparative electrostatic simulation, which confirms that the
electromagnetic simulation is necessary for a higher fidelity understanding of
the electron particle and heat transport even at the low-beta pedestal foot in
the vicinity of the magnetic separatrix.


title: Graviton noise:the Heisenberg picture

abstract:
  We study the geodesic deviation equation for a quantum particle in a
linearized quantum gravitational field. Particle's Heisenberg equations of
motion are treated as stochastic equations with a quantum noise. We explore the
stochastic equation beyond its local approximation as a differential. We
discuss the squeezed states resulting from an inflationary evolution. We
calculate the noise in the thermal and squeezed states.


title:
On the Use of the Microtremor HVSR for Tracking Velocity Changes: A case
  study in Campo de Dal\'ias basin (SE Spain)

abstract:
  The stability of the low-frequency peaks (< 1 Hz) obtained in the passive
seismic survey of Campo de Dal\'ias basin (CDB) by applying the
horizontal-to-vertical spectral ratio (HVSR) method was investigated. Three
temporary seismic stations were installed in remote sites that enabled studying
the stationarity of their characteristic microtremor HVSR (MHVSR) shapes. All
stations began to operate in mid-2016 and recorded at least one year of
continuous seismic ambient noise data, having up to two years in some. Each
seismic station counted with a monitored borehole in their vicinity,
registering the groundwater level every 30 minutes. The MHVSR curves were
calculated for time windows of 150 s and averaged hourly. Four parameters have
been defined to characterize the shape of the MHVSR around the main peak and to
compare them with several environmental variables. Correlations between MHVSR
characteristics and the groundwater level showed to be the most persistent. The
robustness of MHVSR method for applications to seismic engineering was not
found to be compromised since the observed variations were within the margins
of acceptable deviations. Our results widen the possibilities of the MHVSR
method from being a reliable predictor for seismic resonance to also being an
autonomous monitoring tool, especially sensitive to the S-wave modifications.


title:
Multicasting in NOMA-Based UAV Networks: Path Design and Throughput
  Maximization

abstract:
  In this paper, we propose a new resource allocation framework for unmanned
aerial vehicle (UAV) assisted multicast wireless networks in which the network
users according to their request are divided into several multicast groups. We
adopt power domain non-orthogonal multiple access (PD-NOMA) as the transmission
technology using which the dedicated signals of multicast groups are
superimposed and transmitted simultaneously as the UAV passes over the
communication area for fixed and mobile users. We discuss the proposed
scenarios from two perspectives, offline and online mode. In offline mode, we
implement the problem for fixed and mobile users whose locations are
predictable (the location of users, over the communication time, is known at
the beginning of the communication time) and in online mode for mobile users
whose locations are unpredictable (the location of users, over the
communication time, is unknown at the beginning of the communication time).
Also, we proposed a scenario in which the online model the number of mobile
users can grow in each time slot. We formulate the problem of joint power
allocation and UAV trajectory design as an optimization problem that is
non-linear and nonconvex for two proposed scenarios. To solve the problem, we
adopt an alternate search method (ASM), successive convex approximation (SCA),
and geometric programming (GP). Using simulation results, the performance of
the proposed scheme is evaluated for different values of the network
parameters.


title:
Grasp-and-Lift Detection from EEG Signal Using Convolutional Neural
  Network

abstract:
  People undergoing neuromuscular dysfunctions and amputated limbs require
automatic prosthetic appliances. In developing such prostheses, the precise
detection of brain motor actions is imperative for the Grasp-and-Lift (GAL)
tasks. Because of the low-cost and non-invasive essence of
Electroencephalography (EEG), it is widely preferred for detecting motor
actions during the controls of prosthetic tools. This article has automated the
hand movement activity viz GAL detection method from the 32-channel EEG
signals. The proposed pipeline essentially combines preprocessing and
end-to-end detection steps, eliminating the requirement of hand-crafted feature
engineering. Preprocessing action consists of raw signal denoising, using
either Discrete Wavelet Transform (DWT) or highpass or bandpass filtering and
data standardization. The detection step consists of Convolutional Neural
Network (CNN)- or Long Short Term Memory (LSTM)-based model. All the
investigations utilize the publicly available WAY-EEG-GAL dataset, having six
different GAL events. The best experiment reveals that the proposed framework
achieves an average area under the ROC curve of 0.944, employing the DWT-based
denoising filter, data standardization, and CNN-based detection model. The
obtained outcome designates an excellent achievement of the introduced method
in detecting GAL events from the EEG signals, turning it applicable to
prosthetic appliances, brain-computer interfaces, robotic arms, etc.


title:
RETE: Retrieval-Enhanced Temporal Event Forecasting on Unified Query
  Product Evolutionary Graph

abstract:
  With the increasing demands on e-commerce platforms, numerous user action
history is emerging. Those enriched action records are vital to understand
users' interests and intents. Recently, prior works for user behavior
prediction mainly focus on the interactions with product-side information.
However, the interactions with search queries, which usually act as a bridge
between users and products, are still under investigated. In this paper, we
explore a new problem named temporal event forecasting, a generalized user
behavior prediction task in a unified query product evolutionary graph, to
embrace both query and product recommendation in a temporal manner. To fulfill
this setting, there involves two challenges: (1) the action data for most users
is scarce; (2) user preferences are dynamically evolving and shifting over
time. To tackle those issues, we propose a novel Retrieval-Enhanced Temporal
Event (RETE) forecasting framework. Unlike existing methods that enhance user
representations via roughly absorbing information from connected entities in
the whole graph, RETE efficiently and dynamically retrieves relevant entities
centrally on each user as high-quality subgraphs, preventing the noise
propagation from the densely evolutionary graph structures that incorporate
abundant search queries. And meanwhile, RETE autoregressively accumulates
retrieval-enhanced user representations from each time step, to capture
evolutionary patterns for joint query and product prediction. Empirically,
extensive experiments on both the public benchmark and four real-world
industrial datasets demonstrate the effectiveness of the proposed RETE method.


title: Adapting reservoir computing to solve the Schr\"odinger equation

abstract:
  Reservoir computing is a machine learning algorithm that excels at predicting
the evolution of time series, in particular, dynamical systems. Moreover, it
has also shown superb performance at solving partial differential equations. In
this work, we adapt this methodology to integrate the time-dependent
Schr\"odinger equation, propagating an initial wavefunction in time. Since such
wavefunctions are complex-valued high-dimensional arrays the reservoir
computing formalism needs to be extended to cope with complex-valued data.
Furthermore, we propose a multi-step learning strategy that avoids overfitting
the training data. We illustrate the performance of our adapted reservoir
computing method by application to four standard problems in molecular
vibrational dynamics.


title: Rotational $K^\alpha$-translators in Minkowski space

abstract:
  A spacelike surface in Minkowski space $\mathbb{R}_1^3$ is called a
$K^\alpha$-translator of the flow by the powers of Gauss curvature if satisfies
$K^\alpha= \langle N,\vec{v}\rangle$, $\alpha \neq 0$, where $K$ is the Gauss
curvature, $N$ is the unit normal vector field and $\vec{v}$ is a direction of
$\mathbb{R}_1^3$. In this paper, we classify all rotational
$K^\alpha$-translators. This classification will depend on the causal character
of the rotation axis. Although the theory of the $K^\alpha$-flow holds for
spacelike surfaces, the equation describing $K^\alpha$-translators is still
valid for timelike surfaces. So we also investigate the timelike rotational
surfaces that satisfy the same prescribing Gauss curvature equation.


title: Spectral actinometry at SMEAR-Estonia

abstract:
  Systematic spectral measurements of downwelling solar radiation, both of
global and diffuse, have been collected in summertime during 8 years in the
hemi-boreal zone in south east Estonia near the SMEAR-Estonia research station.
The measurements provided information about the variation of spectral and
total, global and diffuse irradiance in the wavelength range from 300 to 2160
nm with spectral resolution of 3 nm in UV to 16 nm in SWIR spectral regions.
Unique data have been collected and quantitative description of the variability
of the measured spectra is provided. For the description of the synoptic
situation during measurements, instead of cloud cover, the ratio of measured to
possible total irradiance in the spectral range of 320--1800 nm is used. This
ratio could be used as the primary meteorological parameter instead of cloud
cover which is difficult to measure instrumentally.


title: Semantic-Oriented Unlabeled Priming for Large-Scale Language Models

abstract:
  Due to the high costs associated with finetuning large language models,
various recent works propose to adapt them to specific tasks without any
parameter updates through in-context learning. Unfortunately, for in-context
learning there is currently no way to leverage unlabeled data, which is often
much easier to obtain in large quantities than labeled examples. In this work,
we therefore investigate ways to make use of unlabeled examples to improve the
zero-shot performance of pretrained language models without any finetuning: We
introduce Semantic-Oriented Unlabeled Priming (SOUP), a method that classifies
examples by retrieving semantically similar unlabeled examples, assigning
labels to them in a zero-shot fashion, and then using them for in-context
learning. We also propose bag-of-contexts priming, a new priming strategy that
is more suitable for our setting and enables the usage of more examples than
fit into the context window.


title:
Algebraic integrability of planar polynomial vector fields by extension
  to Hirzebruch surfaces

abstract:
  We study algebraic integrability of complex planar polynomial vector fields
$X=A (x,y)(\partial/\partial x) + B(x,y) (\partial/\partial y) $ through
extensions to Hirzebruch surfaces. Using these extensions, each vector field
$X$ determines two infinite families of planar vector fields that depend on a
natural parameter which, when $X$ has a rational first integral, satisfy strong
properties about the dicriticity of the points at the line $x=0$ and of the
origin. As a consequence, we obtain new necessary conditions for algebraic
integrability of planar vector fields and, if $X$ has a rational first
integral, we provide a region in $\mathbb{R}_{\geq 0}^2$ that contains all the
pairs $(i,j)$ corresponding to monomials $x^i y^j$ involved in the generic
invariant curve of $X$.


title: Online Bayesian Recommendation with No Regret

abstract:
  We introduce and study the online Bayesian recommendation problem for a
platform, who can observe a utility-relevant state of a product, repeatedly
interacting with a population of myopic users through an online recommendation
mechanism. This paradigm is common in a wide range of scenarios in the current
Internet economy. For each user with her own private preference and belief, the
platform commits to a recommendation strategy to utilize his information
advantage on the product state to persuade the self-interested user to follow
the recommendation. The platform does not know user's preferences and beliefs,
and has to use an adaptive recommendation strategy to persuade with gradually
learning user's preferences and beliefs in the process.
  We aim to design online learning policies with no Stackelberg regret for the
platform, i.e., against the optimum policy in hindsight under the assumption
that users will correspondingly adapt their behaviors to the benchmark policy.
Our first result is an online policy that achieves double logarithm regret
dependence on the number of rounds. We then present a hardness result showing
that no adaptive online policy can achieve regret with better dependency on the
number of rounds. Finally, by formulating the platform's problem as optimizing
a linear program with membership oracle access, we present our second online
policy that achieves regret with polynomial dependence on the number of states
but logarithm dependence on the number of rounds.


title:
Littlewood-Paley functions associated with general Ornstein-Uhlenbeck
  semigroups

abstract:
  In this paper we establish $L^p(\mathbb{R}^d,\gamma_\infty)$-boundedness
properties for square functions involving time and spatial derivatives of
Ornstein-Uhlenbeck semigroups. Here $\gamma_\infty$ denotes the invariant
measure. In order to prove the strong type results for $1<p<\infty$ we use
$R$-boundedness. The weak type (1,1) property is established by studying
separately global and local operators defined for the square Littlewood-Paley
functions. By the way we prove $L^p(\mathbb{R}^d,\gamma_\infty)$-boundedness
properties for maximal and variation operators for Ornstein-Uhlenbeck
semigroups.


title: MIONet: Learning multiple-input operators via tensor product

abstract:
  As an emerging paradigm in scientific machine learning, neural operators aim
to learn operators, via neural networks, that map between infinite-dimensional
function spaces. Several neural operators have been recently developed.
However, all the existing neural operators are only designed to learn operators
defined on a single Banach space, i.e., the input of the operator is a single
function. Here, for the first time, we study the operator regression via neural
networks for multiple-input operators defined on the product of Banach spaces.
We first prove a universal approximation theorem of continuous multiple-input
operators. We also provide detailed theoretical analysis including the
approximation error, which provides a guidance of the design of the network
architecture. Based on our theory and a low-rank approximation, we propose a
novel neural operator, MIONet, to learn multiple-input operators. MIONet
consists of several branch nets for encoding the input functions and a trunk
net for encoding the domain of the output function. We demonstrate that MIONet
can learn solution operators involving systems governed by ordinary and partial
differential equations. In our computational examples, we also show that we can
endow MIONet with prior knowledge of the underlying system, such as linearity
and periodicity, to further improve the accuracy.


title: An exactly solvable predator prey model with resetting

abstract:
  We study a simple model of a diffusing particle (the prey) that on encounter
with one of a swarm of diffusing predators can either perish or be reset to its
original position at the origin. We show that the survival probability of the
prey up to time $t$ decays algebraically as $\sim t^{-\theta(p, \gamma)}$ where
the exponent $\theta$ depends continuously on two parameters of the model, with
$p$ denoting the probability that a prey survives upon encounter with a
predator and $\gamma = D_A/(D_A+D_B)$ where $D_A$ and $D_B$ are the diffusion
constants of the prey and the predator respectively. We also compute exactly
the probability distribution $P(N|t_c)$ of the total number of encounters till
the capture time $t_c$ and show that it exhibits an anomalous large deviation
form $P(N|t_c)\sim t_c^{- \Phi\left(\frac{N}{\ln t_c}=z\right)}$ for large
$t_c$. The rate function $\Phi(z)$ is computed explicitly. Numerical
simulations are in excellent agreement with our analytical results.


title:
A Data-driven Multi-fidelity Physics-informed Learning Framework for
  Smart Manufacturing: A Composites Processing Case Study

abstract:
  Despite the successful implementations of physics-informed neural networks in
different scientific domains, it has been shown that for complex nonlinear
systems, achieving an accurate model requires extensive hyperparameter tuning,
network architecture design, and costly and exhaustive training processes. To
avoid such obstacles and make the training of physics-informed models less
precarious, in this paper, a data-driven multi-fidelity physics-informed
framework is proposed based on transfer learning principles. The framework
incorporates the knowledge from low-fidelity auxiliary systems and limited
labeled data from target actual system to significantly improve the performance
of conventional physics-informed models. While minimizing the efforts of
designing a complex task-specific network for the problem at hand, the proposed
settings guide the physics-informed model towards a fast and efficient
convergence to a global optimum. An adaptive weighting method is utilized to
further enhance the optimization of the model composite loss function during
the training process. A data-driven strategy is also introduced for maintaining
high performance in subdomains with significant divergence between low- and
high-fidelity behaviours. The heat transfer of composite materials undergoing a
cure cycle is investigated as a case study to demonstrate the proposed
framework's performance compared to conventional physics-informed models.


title:
Grasp Control of a Cable-Driven Robotic Hand Using a PVDF Slip Detection
  Sensor

abstract:
  Detecting and preventing slip is a major challenge in robotic hand operation,
underpinning the robot's ability to perform safe and reliable grasps. Using the
robotic hand design from the authors' earlier work, a sensing and control
strategy is proposed here to prevent object slippage. The robotic hand is
cable-driven, single-actuated, has five fingers, and is capable of replicating
most human hand motions. The slip sensing approach utilizes a piezoelectric
vibration sensor, namely, polyvinylidene fluoride (PVDF), which is a flexible,
thin, cheap, and highly sensitive material. The power of the filtered PVDF
signal is shown to exhibit identifiable signatures during slip, thus providing
a suitable slip detection mechanism. Using the PVDF feedback, an integral
controller is implemented to prevent the grasped object from falling and ensure
a safe, powerful, and reliable grasp. The extension movement of the robotic
hand is controlled using a bend sensor, through a proportional-integral (PI)
controller. The robotic hand weights 338 gr. The functionality and robustness
of the proposed slip-detection sensory system and control logic implementation
are evaluated through experiments.


title:
Sparse Training with Lipschitz Continuous Loss Functions and a Weighted
  Group L0-norm Constraint

abstract:
  This paper is motivated by structured sparsity for deep neural network
training. We study a weighted group L0-norm constraint, and present the
projection and normal cone of this set. Using randomized smoothing, we develop
zeroth and first-order algorithms for minimizing a Lipschitz continuous
function constrained by any closed set which can be projected onto.
Non-asymptotic convergence guarantees are proven in expectation for the
proposed algorithms for two related convergence criteria which can be
considered as approximate stationary points. Two further methods are given
using the proposed algorithms: one with non-asymptotic convergence guarantees
in high probability, and the other with asymptotic guarantees to a stationary
point almost surely. We believe in particular that these are the first such
non-asymptotic convergence results for constrained Lipschitz continuous loss
functions.


title:
Multi-task Deep Learning for Cerebrovascular Disease Classification and
  MRI-to-PET Translation

abstract:
  Accurate quantification of cerebral blood flow (CBF) is essential for the
diagnosis and assessment of cerebrovascular diseases such as Moyamoya, carotid
stenosis, aneurysms, and stroke. Positron emission tomography (PET) is
currently regarded as the gold standard for the measurement of CBF in the human
brain. PET imaging, however, is not widely available because of its prohibitive
costs, use of ionizing radiation, and logistical challenges, which require a
co-localized cyclotron to deliver the 2 min half-life Oxygen-15 radioisotope.
Magnetic resonance imaging (MRI), in contrast, is more readily available and
does not involve ionizing radiation. In this study, we propose a multi-task
learning framework for brain MRI-to-PET translation and disease diagnosis. The
proposed framework comprises two prime networks: (1) an attention-based 3D
encoder-decoder convolutional neural network (CNN) that synthesizes
high-quality PET CBF maps from multi-contrast MRI images, and (2) a multi-scale
3D CNN that identifies the brain disease corresponding to the input MRI images.
Our multi-task framework yields promising results on the task of MRI-to-PET
translation, achieving an average structural similarity index (SSIM) of 0.94
and peak signal-to-noise ratio (PSNR) of 38dB on a cohort of 120 subjects. In
addition, we show that integrating multiple MRI modalities can improve the
clinical diagnosis of brain diseases.


title:
Stochastic Strategic Patient Buyers: Revenue maximization using posted
  prices

abstract:
  We consider a seller faced with buyers which have the ability to delay their
decision, which we call patience. Each buyer's type is composed of value and
patience, and it is sampled i.i.d. from a distribution. The seller, using
posted prices, would like to maximize her revenue from selling to the buyer.
Our main results are the following.
  $\bullet$ We formalize this setting and characterize the resulting
Stackelberg equilibrium, where the seller first commits to her strategy and
then the buyers best respond.
  $\bullet$ We show a separation between the best fixed price, the best pure
strategy, which is a fixed sequence of prices, and the best mixed strategy,
which is a distribution over price sequences.
  $\bullet$ We characterize both the optimal pure strategy of the seller and
the buyer's best response strategy to any seller's mixed strategy.
  $\bullet$ We show how to compute efficiently the optimal pure strategy and
give an algorithm for the optimal mixed strategy (which is exponential in the
maximum patience).
  We then consider a learning setting, where the seller does not have access to
the distribution over buyer's types. Our main results are the following.
  $\bullet$ We derive a sample complexity bound for the learning of an
approximate optimal pure strategy, by computing the fat-shattering dimension of
this setting.
  $\bullet$ We give a general sample complexity bound for the approximate
optimal mixed strategy.
  $\bullet$ We consider an online setting and derive a vanishing regret bound
with respect to both the optimal pure strategy and the optimal mixed strategy.


title: Suslin tree preservation and club isomorphisms

abstract:
  We construct a model of set theory in which there exists a Suslin tree and
satisfies that any two normal Aronszajn trees, neither of which contains a
Suslin subtree, are club isomorphic. We also show that if $S$ is a free normal
Suslin tree, then for any positive integer $n$ there is a c.c.c. forcing
extension in which $S$ is $n$-free but all of its derived trees of dimension
greater than $n$ are special.


title:
Revisiting the Impact of Dependency Network Metrics on Software Defect
  Prediction

abstract:
  Software dependency network metrics extracted from the dependency graph of
the software modules by the application of Social Network Analysis (SNA
metrics) have been shown to improve the performance of the Software Defect
prediction (SDP) models. However, the relative effectiveness of these SNA
metrics over code metrics in improving the performance of the SDP models has
been widely debated with no clear consensus. Furthermore, some of the common
SDP scenarios like predicting the number of defects in a module (Defect-count)
in Cross-version and Cross-project SDP contexts remain unexplored. Such lack of
clear directive on the effectiveness of SNA metrics when compared to the widely
used code metrics prevents us from potentially building better performing SDP
models. Therefore, through a case study of 9 open source software projects
across 30 versions, we study the relative effectiveness of SNA metrics when
compared to code metrics across 3 commonly used SDP contexts (Within-project,
Cross-version and Cross-project) and scenarios (Defect-count,
Defect-classification (classifying if a module is defective) and Effort-aware
(ranking the defective modules w.r.t to the involved effort)). We find the SNA
metrics by themselves or along with code metrics improve the performance of SDP
models over just using code metrics on 5 out of the 9 studied SDP scenarios
(three SDP scenarios across three SDP contexts). However, we note that in some
cases the improvements afforded by considering SNA metrics over or alongside
code metrics might only be marginal, whereas in other cases the improvements
could be potentially large. Based on these findings we suggest that the future
work should: consider SNA metrics alongside code metrics in their SDP models;
as well as consider Ego metrics and Global metrics, the two different types of
the SNA metrics separately when training SDP models as they behave differently.


title:
Impact of Discretization Noise of the Dependent variable on Machine
  Learning Classifiers in Software Engineering

abstract:
  Researchers usually discretize a continuous dependent variable into two
target classes by introducing an artificial discretization threshold (e.g.,
median). However, such discretization may introduce noise (i.e., discretization
noise) due to ambiguous class loyalty of data points that are close to the
artificial threshold. Previous studies do not provide a clear directive on the
impact of discretization noise on the classifiers and how to handle such noise.
In this paper, we propose a framework to help researchers and practitioners
systematically estimate the impact of discretization noise on classifiers in
terms of its impact on various performance measures and the interpretation of
classifiers. Through a case study of 7 software engineering datasets, we find
that: 1) discretization noise affects the different performance measures of a
classifier differently for different datasets; 2) Though the interpretation of
the classifiers are impacted by the discretization noise on the whole, the top
3 most important features are not affected by the discretization noise.
Therefore, we suggest that practitioners and researchers use our framework to
understand the impact of discretization noise on the performance of their built
classifiers and estimate the exact amount of discretization noise to be
discarded from the dataset to avoid the negative impact of such noise.


title: Phase retrieval from angular streaking of XUV atomic ionization

abstract:
  We demonstrate an accurate phase retrieval of XUV atomic ionization by
streaking the photoelectron in a circularly polarized IR laser field. The
streaking phase can then be converted to the atomic time delay containing the
Wigner and continuum-continuum components. Our demonstration is based on a
numerical solution of the time-dependent Schr\"odinger equation. We test this
technique using the hydrogen atom ionized by an isolated attosecond XUV pulse
across a wide range of photon energies. In parallel, we run a series of RABBITT
simulations and demonstrate equivalence of the phase and timing information
provided by the two methods. This validates the proposed technique and makes it
a useful tool that can be applied to a broad range of atomic and molecular
targets exposed to XUV radiation from novel free-electron laser sources.


title:
Study of Robust Adaptive Power allocation for the Downlink of
  Multiple-Antenna Systems

abstract:
  Multiple-input multiple-output (MIMO) systems greatly increase the overall
throughput of wireless systems since they are capable of transmitting multiple
streams employing the same time-frequency resources. However, this gain
requires an appropriate precoder design and a power allocation technique. In
general, precoders and power allocation schemes are designed assuming perfect
channel estate information (CSI). Nonetheless, this is an optimistic assumption
since real systems only possess partial or imperfect CSI at the transmitter
(CSIT). The imperfect CSIT originates residual inter-user interference, which
is detrimental for wireless systems. In this paper, two adaptive power
allocation algorithms are proposed, which are more robust against CSIT
imperfections than conventional techniques. Both techniques employ the mean
square error as the objective function. Simulation results show that the
proposed techniques obtain a higher performance in terms of sum-rate than
conventional approaches.


title:
Automatic Issue Classifier: A Transfer Learning Framework for
  Classifying Issue Reports

abstract:
  Issue tracking systems are used in the software industry for the facilitation
of maintenance activities that keep the software robust and up to date with
ever-changing industry requirements. Usually, users report issues that can be
categorized into different labels such as bug reports, enhancement requests,
and questions related to the software. Most of the issue tracking systems make
the labelling of these issue reports optional for the issue submitter, which
leads to a large number of unlabeled issue reports. In this paper, we present a
state-of-the-art method to classify the issue reports into their respective
categories i.e. bug, enhancement, and question. This is a challenging task
because of the common use of informal language in the issue reports. Existing
studies use traditional natural language processing approaches adopting
key-word based features, which fail to incorporate the contextual relationship
between words and therefore result in a high rate of false positives and false
negatives. Moreover, previous works utilize a uni-label approach to classify
the issue reports however, in reality, an issue-submitter can tag one issue
report with more than one label at a time. This paper presents our approach to
classify the issue reports in a multi-label setting. We use an off-the-shelf
neural network called RoBERTa and fine-tune it to classify the issue reports.
We validate our approach on issue reports belonging to numerous industrial
projects from GitHub. We were able to achieve promising F-1 scores of 81%, 74%,
and 80% for bug reports, enhancements, and questions, respectively. We also
develop an industry tool called Automatic Issue Classifier (AIC), which
automatically assigns labels to newly reported issues on GitHub repositories
with high accuracy.


title: Adaptive Bandit Convex Optimization with Heterogeneous Curvature

abstract:
  We consider the problem of adversarial bandit convex optimization, that is,
online learning over a sequence of arbitrary convex loss functions with only
one function evaluation for each of them. While all previous works assume known
and homogeneous curvature on these loss functions, we study a heterogeneous
setting where each function has its own curvature that is only revealed after
the learner makes a decision. We develop an efficient algorithm that is able to
adapt to the curvature on the fly. Specifically, our algorithm not only
recovers or \emph{even improves} existing results for several homogeneous
settings, but also leads to surprising results for some heterogeneous settings
-- for example, while Hazan and Levy (2014) showed that
$\widetilde{O}(d^{3/2}\sqrt{T})$ regret is achievable for a sequence of $T$
smooth and strongly convex $d$-dimensional functions, our algorithm reveals
that the same is achievable even if $T^{3/4}$ of them are not strongly convex,
and sometimes even if a constant fraction of them are not strongly convex. Our
approach is inspired by the framework of Bartlett et al. (2007) who studied a
similar heterogeneous setting but with stronger gradient feedback. Extending
their framework to the bandit feedback setting requires novel ideas such as
lifting the feasible domain and using a logarithmically homogeneous
self-concordant barrier regularizer.


title:
Corralling a Larger Band of Bandits: A Case Study on Switching Regret
  for Linear Bandits

abstract:
  We consider the problem of combining and learning over a set of adversarial
bandit algorithms with the goal of adaptively tracking the best one on the fly.
The CORRAL algorithm of Agarwal et al. (2017) and its variants (Foster et al.,
2020a) achieve this goal with a regret overhead of order
$\widetilde{O}(\sqrt{MT})$ where $M$ is the number of base algorithms and $T$
is the time horizon. The polynomial dependence on $M$, however, prevents one
from applying these algorithms to many applications where $M$ is poly$(T)$ or
even larger. Motivated by this issue, we propose a new recipe to corral a
larger band of bandit algorithms whose regret overhead has only
\emph{logarithmic} dependence on $M$ as long as some conditions are satisfied.
As the main example, we apply our recipe to the problem of adversarial linear
bandits over a $d$-dimensional $\ell_p$ unit-ball for $p \in (1,2]$. By
corralling a large set of $T$ base algorithms, each starting at a different
time step, our final algorithm achieves the first optimal switching regret
$\widetilde{O}(\sqrt{d S T})$ when competing against a sequence of comparators
with $S$ switches (for some known $S$). We further extend our results to linear
bandits over a smooth and strongly convex domain as well as unconstrained
linear bandits.


title:
From Online Optimization to PID Controllers: Mirror Descent with
  Momentum

abstract:
  We study a family of first-order methods with momentum based on mirror
descent for online convex optimization, which we dub online mirror descent with
momentum (OMDM). Our algorithms include as special cases gradient descent and
exponential weights update with momentum. We provide a new and simple analysis
of momentum-based methods in a stochastic setting that yields a regret bound
that decreases as momentum increases. This immediately establishes that
momentum can help in the convergence of stochastic subgradient descent in
convex nonsmooth optimization. We showcase the robustness of our algorithm by
also providing an analysis in an adversarial setting that gives the first
non-trivial regret bounds for OMDM. Our work aims to provide a better
understanding of the benefits of momentum-based methods, which despite their
recent empirical success, is incomplete.
  Finally, we discuss how OMDM can be applied to stochastic online allocation
problems, which are central problems in computer science and operations
research. In doing so, we establish an important connection between OMDM and
popular approaches from optimal control such as PID controllers, thereby
providing regret bounds on the performance of PID controllers. The improvements
of momentum are most pronounced when the step-size is large, thereby indicating
that momentum provides a robustness to misspecification of tuning parameters.
We provide a numerical evaluation that verifies the robustness of our
algorithms.


title: A $q$-deformation of enriched $P$-partitions (extended abstract)

abstract:
  We introduce a $q$-deformation that generalises in a single framework
previous works on classical and enriched $P$-partitions. In particular, we
build a new family of power series with a parameter $q$ that interpolates
between Gessel's fundamental ($q=0$) and Stembridge's peak quasisymmetric
functions ($q=1$) and show that it is a basis of $\QSym$ when
$q\notin\{-1,1\}$. Furthermore we build their corresponding monomial bases
parametrised with $q$ that cover our previous work on enriched monomials and
the essential quasisymmetric functions of Hoffman.


title:
Generalization of the Landau-Lifshitz-Gilbert equation by multi-body
  contributions to Gilbert damping for non-collinear magnets

abstract:
  We propose a systematic and sequential expansion of the
Landau-Lifshitz-Gilbert equation utilizing the dependence of the Gilbert
damping tensor on the angle between magnetic moments, which arises from
multi-body scattering processes. The tensor consists of a damping-like term and
a correction to the gyromagnetic ratio. Based on electronic structure theory,
both terms are shown to depend on e.g. the scalar, anisotropic, vector-chiral
and scalar-chiral products of magnetic moments: $\vec{e}_i\cdot\vec{e}_j$,
$(\vec{n}_{ij}\cdot\vec{e}_i)(\vec{n}_{ij}\cdot\vec{e}_j)$,
$\vec{n}_{ij}\cdot(\vec{e}_i\times\vec{e}_j)$, $(\vec{e}_i\cdot\vec{e}_j)^2$,
$\vec{e}_i\cdot(\vec{e}_j\times\vec{e}_k)$..., where some terms are subjected
to the spin-orbit field $\vec{n}_{ij}$ in first and second order. We explore
the magnitude of the different contributions using both the Alexander-Anderson
model and time-dependent density functional theory in magnetic adatoms and
dimers deposited on Au(111) surface.


title:
Knitting quantum knots: Topological phase transitions in Two-Dimensional
  systems

abstract:
  We start by describing a symmetry enforced nodal line semi-metal (NLSM) in
the 2D flat form of honeycomb Group - V and its non trivial thermo-electric
response. We will then proceed to show that, upon buckling, the system
undergoes its dirac-merging phase transitions. Further buckling leads to these
unpinned Dirac cones annihilating in pairs at two distinct critical angle
leading to a second topological phase transition to an insulating state. We
then show that this seemingly innocuous insulating state is indeed a weak
topological crystalline insulator. Furthermore, upon closer look, this
insulating state turns out to be a Higher Order Topological Insulator (HOTI)
that is protected by $\mathcal{S}_6$ symmetry. In a broader context, we will
see that the the topological properties of buckled Group - $V$ stem from the
fact that they topologically belong to the class of Obstructed Atomic Limit
(OAL) insulators. Combining all these, we will prove that annihilating pairs of
Dirac fermions necessitate a topological phase transition from the critical
semi-metallic phase to an OAL insulator phase. We also uncover the rich set of
phases in the phase diagram in case of annihilating Dirac fermions and study
their entanglement properties using entanglement entropy. Finally, based on the
non-trivial topology of these systems, we propose the conceptual design of a
quantized switch that is protected by topology. Last part of the thesis
involves the remarkable discovery of a spin polarized 2D electron/hole gas at
the surfaces of a well known system - LiCoO2.


title:
Numerical scheme for Erd\'elyi-Kober fractional diffusion equation using
  Galerkin-Hermite method

abstract:
  The aim of this work is to devise and analyse an accurate numerical scheme to
solve Erd\'elyi-Kober fractional diffusion equation. This solution can be
thought as the marginal pdf of the stochastic process called the generalized
grey Brownian motion (ggBm). The ggBm includes some well-known stochastic
processes: Brownian motion, fractional Brownian motion and grey Brownian
motion. To obtain convergent numerical scheme we transform the fractional
diffusion equation into its weak form and apply the discretization of the
Erd\'elyi-Kober fractional derivative. We prove the stability of the solution
of the semi-discrete problem and its convergence to the exact solution. Due to
the singular in time term appearing in the main equation the proposed method
converges slower than first order. Finally, we provide the numerical analysis
of the full-discrete problem using orthogonal expansion in terms of Hermite
functions.


title: The Impact of Using Regression Models to Build Defect Classifiers

abstract:
  It is common practice to discretize continuous defect counts into defective
and non-defective classes and use them as a target variable when building
defect classifiers (discretized classifiers). However, this discretization of
continuous defect counts leads to information loss that might affect the
performance and interpretation of defect classifiers. Another possible approach
to build defect classifiers is through the use of regression models then
discretizing the predicted defect counts into defective and non-defective
classes (regression-based classifiers).
  In this paper, we compare the performance and interpretation of defect
classifiers that are built using both approaches (i.e., discretized classifiers
and regression-based classifiers) across six commonly used machine learning
classifiers (i.e., linear/logistic regression, random forest, KNN, SVM, CART,
and neural networks) and 17 datasets. We find that: i) Random forest based
classifiers outperform other classifiers (best AUC) for both classifier
building approaches; ii) In contrast to common practice, building a defect
classifier using discretized defect counts (i.e., discretized classifiers) does
not always lead to better performance.
  Hence we suggest that future defect classification studies should consider
building regression-based classifiers (in particular when the defective ratio
of the modeled dataset is low). Moreover, we suggest that both approaches for
building defect classifiers should be explored, so the best-performing
classifier can be used when determining the most influential features.


title:
Phase Diagrams of Kitaev Models for Arbitrary Magnetic-Field
  Orientations

abstract:
  The Kitaev model is an exactly solvable quantum spin model within the
language of the constrained real fermions. In spite of numerous studies along
special magnetic-field orientations, there is a limited amount of knowledge on
the complete field-angle characterization, which can provide valuable
information on the existence of fractionalized excitations. For this purpose,
we first extend previous studies on the field-angle response of the
ferromagnetic Kitaev model to its antiferromagnetic version. Yet, the realistic
description of the candidate Kitaev materials, within the edge-sharing
octahedra paradigm, require additional coupling terms, including a large
off-diagonal term $\Gamma$ along with possible anisotropic corrections
$\Gamma_p$. It is therefore not sufficient to depend on the topological
properties of the bare Kitaev model as the only source for the observed thermal
Hall conductivity signals and an understanding of these extended Kitaev models
with a complete field response is demanded. Starting from the zero-field phase
diagram of realistic K-$\Gamma$-$\Gamma_p$ models, we identify
antiferromagnetic zig-zag and (partially) polarized phases as well as two
unusual Kitaev(-$\Gamma$) spin-liquid phases. The magnetic field response of
these phases for arbitrary field orientations provides a remarkably rich phase
diagram. A partially polarized phase is revealed between two ordered phases
with a suppressed magnetization, finite fractionalization and finite Chern
number. This phase is characterized as an extended Kitaev-$\Gamma$ spin-liquid.
To comply our findings with experiments, we reproduce the asymmetry in the
extent of the intermediate phases specifically for the two different field
directions $\theta = \pm 60^o$.


title:
Robust alignment of cross-session recordings of neural population
  activity by behaviour via unsupervised domain adaptation

abstract:
  Neural population activity relating to behaviour is assumed to be inherently
low-dimensional despite the observed high dimensionality of data recorded using
multi-electrode arrays. Therefore, predicting behaviour from neural population
recordings has been shown to be most effective when using latent variable
models. Over time however, the activity of single neurons can drift, and
different neurons will be recorded due to movement of implanted neural probes.
This means that a decoder trained to predict behaviour on one day performs
worse when tested on a different day. On the other hand, evidence suggests that
the latent dynamics underlying behaviour may be stable even over months and
years. Based on this idea, we introduce a model capable of inferring
behaviourally relevant latent dynamics from previously unseen data recorded
from the same animal, without any need for decoder recalibration. We show that
unsupervised domain adaptation combined with a sequential variational
autoencoder, trained on several sessions, can achieve good generalisation to
unseen data and correctly predict behaviour where conventional methods fail.
Our results further support the hypothesis that behaviour-related neural
dynamics are low-dimensional and stable over time, and will enable more
effective and flexible use of brain computer interface technologies.


title:
Hamiltonian approach for point vortices on non-orientable surfaces I:
  the Mobius band

abstract:
  This is the first of two companion papers, in which we investigate vortex
motion on non-orientable two dimensional surfaces. We establish the
`Hamiltonian' approach to point vortex motion on non-orientable surfaces
through describing the phase space, the Hamiltonian and the local equations of
motion. This paper is primarily focused on the dynamics on the Mobius band. To
this end, we adapt some of the known notions of vortex dynamics to
non-orientable surfaces. We write Hamiltonian-type equations of vortex motion
explicitly and follow that by the description of relative equilibria and a
thorough investigation of motion of one and two vortices, with emphasis on the
periodicity of motion.


title: Characterizing unit spheres in Euclidean spaces via reach and volume

abstract:
  Let $M$ be a smooth, connected, compact submanifold of $\mathbb{R}^n$ without
boundary and of dimension $k\geq 2$. Let $\mathbb{S}^k \subset
\mathbb{R}^{k+1}\subset \mathbb{R}^n$ denote the $k$-dimesnional unit sphere.
We show if $M$ has reach equal to one, then its volume satisfies
$\text{vol}(M)\geq \text{vol}(\mathbb{S}^k)$ with equality holding only if $M$
is congruent to $\mathbb{S}^k$.


title: Formation and dynamics of a semi vortex ring connected to a free surface

abstract:
  Playing a role in the locomotion of some animals such as the water strider,
the formation and dynamics of a semi vortex ring connected to a free surface
are experimentally investigated. This semi vortex ring is generated by the
circular motion of a flat circular disk in water. Digital Particle Image
Velocimetry provides velocity fields and vortex properties. We show how in a
broad range of Reynolds numbers, the properties of the semi vortex rings are
related to the disk characteristics. In particular, our results highlight a
formation process more complex than for a complete vortex ring produced by a
piston stroke. In addition to the classical rolling up at the rear of the disk,
a shedding phenomenon occurs on the leading edge, producing secondary vortices.
The Strouhal number related to this shedding process reveals that it comes from
the free-shear instability of the boundary layer identified in the near wake of
a cylinder by Bloor. Finally we show that the disk thickness affects the final
properties of the semi vortex rings through emission frequency of secondary
vortices.


title:
Evolving Neural Networks with Optimal Balance between Information Flow
  and Connections Cost

abstract:
  Evolving Neural Networks (NNs) has recently seen an increasing interest as an
alternative path that might be more successful. It has many advantages compared
to other approaches, such as learning the architecture of the NNs. However, the
extremely large search space and the existence of many complex interacting
parts still represent a major obstacle. Many criteria were recently
investigated to help guide the algorithm and to cut down the large search
space. Recently there has been growing research bringing insights from network
science to improve the design of NNs. In this paper, we investigate evolving
NNs architectures that have one of the most fundamental characteristics of
real-world networks, namely the optimal balance between connections cost and
information flow. The performance of different metrics that represent this
balance is evaluated and the improvement in the accuracy of putting more
selection pressure toward this balance is demonstrated on three datasets.


title:
Complete Inertial Pose Dataset: from raw measurements to pose with
  low-cost and high-end MARG sensors

abstract:
  The use of wearable technology for posture monitoring has been expanding due
to its low-intrusiveness and compliance with daily use requirements. However,
there are still open challenges limiting its widespread use, especially when
dealing with low-cost systems. Most solutions falls either into fully
functioning commercial products with high costs, or ad-hoc solutions with lower
performance. Moreover, there are few datasets available, from which complete
and general solutions can be derived. This work presents 2 datasets, containing
low-cost and high-end Magnetic, Angular Rate, and Gravity (MARG) sensor data
respectively. It provides data for the analysis of the complete inertial pose
pipeline, from raw measurements, to sensor-to-segment calibration, multi-sensor
fusion, skeleton kinematics, to the complete human pose. Multiple trials were
collected with 21 and 10 subjects respectively, performing 6 types of sequences
(ranging from calibration, to daily-activities and random movements). It
presents a high degree of variability and complex dynamics with almost complete
range-of-motion, while containing common sources of error found on real
conditions. This amounts to 3.5M samples, synchronized with a ground-truth
inertial motion capture system at 60hz. A simple end-to-end inertial pose
method was briefly described and used to validate the quality of the data in
both acquisitions. This database may contribute to assess, benchmark and
develop novel algorithms for each of the pipelines' processing steps, with
applications in classic or data-driven inertial pose estimation algorithms,
human movement understanding and forecasting and ergonomic assessment in
industrial or rehabilitation settings. All the data is freely available on an
online database and accompanied with code to process and analyze the complete
data pipeline.


title:
InfraredTags: Embedding Invisible AR Markers and Barcodes Using
  Low-Cost, Infrared-Based 3D Printing and Imaging Tools

abstract:
  Existing approaches for embedding unobtrusive tags inside 3D objects require
either complex fabrication or high-cost imaging equipment. We present
InfraredTags, which are 2D markers and barcodes imperceptible to the naked eye
that can be 3D printed as part of objects, and detected rapidly by low-cost
near-infrared cameras. We achieve this by printing objects from an
infrared-transmitting filament, which infrared cameras can see through, and by
having air gaps inside for the tag's bits, which appear at a different
intensity in the infrared image.
  We built a user interface that facilitates the integration of common tags (QR
codes, ArUco markers) with the object geometry to make them 3D printable as
InfraredTags. We also developed a low-cost infrared imaging module that
augments existing mobile devices and decodes tags using our image processing
pipeline. Our evaluation shows that the tags can be detected with little
near-infrared illumination (0.2lux) and from distances as far as 250cm. We
demonstrate how our method enables various applications, such as object
tracking and embedding metadata for augmented reality and tangible
interactions.