title:
Geometric Corroboration of the Earliest Lensed Galaxy at z~10.8 from
  Robust Free-Form Modelling

abstract:
  A multiply-lensed galaxy, MACS0647-JD, with a probable photometric redshift
of $z\simeq 10.7^{+0.6}_{-0.4}$ is claimed to constitute one of the very
earliest known galaxies, formed well before reionization was completed.
However, spectral evidence that MACS0647-JD lies at high redshift has proven
infeasible and so here we seek an independent lensing based "geometric
redshift" derived from the angles between the three lensed images of
MACS0647-JD, using our free-form mass model (WSLAP+) for the lensing cluster
MACSJ0647.7+7015 (at $z=0.591$). Our lens model uses the 9 sets of multiple
images, including those of MACS0647-JD, identified by the CLASH survey towards
this cluster. We convincingly exclude the low redshift regime of $z<3$, for
which convoluted critical curves are generated by our method, as the solution
bends to accommodate the wide angles of MACS0647-JD for this low redshift.
Instead, a best fit to all sets of lensed galaxy positions and redshifts
provides a geometric redshift of $z\simeq 10.8^{+0.3}_{-0.4}$ for MACS0647-JD,
strongly supporting the higher photometric redshift solution. Importantly, we
find a tight linear relation between the relative brightnesses of all 9 sets of
multiply lensed images and their relative magnifications as predicted by our
model. This agreement provides a benchmark for the quality of the lens model,
and establishes the robustness of our free-form lensing method for measuring
model-independent geometric source distances and for deriving objective central
cluster mass distributions. After correcting for its magnification the
luminosity of MACS0647-JD remains relatively high at $M_{UV}=-19.4$, which is
within a factor of a few in flux of some surprisingly luminous $z\simeq
10$--$11$ candidates discovered recently in Hubble black field surveys.


title:
Construction of Multi-Chromophoric Spectra from Monomer Data:
  Applications to Resonant Energy Transfer

abstract:
  We develop a model that establishes a quantitative link between the physical
properties of molecular aggregates and their constituent building blocks. The
relation is built on the coherent potential approximation, calibrated against
exact results, and proven reliable for a wide range of parameters. It provides
a practical method to compute spectra and transfer rates in multi-chromophoric
systems from experimentally accessible monomer data. Applications to F\"orster
energy transfer reveal optimal transfer rates as functions of both the
system-bath coupling and intra-aggregate coherence.


title: Nowhere-zero flows in signed graphs: A survey

abstract:
  We survey known results related to nowhere-zero flows and related topics,
such as circuit covers and the structure of circuits of signed graphs. We
include an overview of several different definitions of signed graph colouring.


title:
Alignment without Decoupling: the Portal to Light Dark Matter in the
  MSSM

abstract:
  We study light, thermal neutralino dark matter in the sub-GeV to 65 GeV mass
range in the Minimal Supersymmetric extension of the Standard Model (MSSM). We
consider realizations of the limit of alignment without decoupling in the Higgs
sector where the heavier CP-even Higgs impersonates the observed Higgs state at
125 GeV, while the lighter CP-even Higgs is the mediator of dark matter
annihilation. We single out three distinct and novel possibilities for light
dark matter: (i) a neutralino with mass around half the light Higgs mass, in
the sub-GeV to 30 GeV mass range; (ii) a neutralino with a mass around half the
pseudoscalar Higgs boson mass, in our examples around 60 to 65 GeV; (iii) a
very light neutralino with mass around the light Higgs mass, pair-annihilating
to Higgs pairs. We discuss the implications of all these possibilities for
indirect and direct dark matter detection experiments, and we demonstrate that
all scenarios will be tested by next generation direct detection experiments.
We also emphasize that the unique Higgs phenomenology of these scenarios
warrants a dedicated search program at the LHC.


title:
Quantized Brans Dicke Theory: Phase Transition and Strong Coupling
  (Large $\omega$) Limit & General Relativity

abstract:
  We show that Friedmann-Robertson-Walker (FRW) geometry with flat spatial
section in quantized (Wheeler deWitt quantization) Brans Dicke (BD) theory
reveals a rich phase structure owing to anomalous breaking of a classical
symmetry, which maps the scale factor $a\mapsto\lambda a$ for some constant
$\lambda$. In the weak coupling ($\omega$) limit, the theory goes from a
symmetry preserving phase to a broken phase. The existence of phase boundary is
an obstruction to another classical symmetry [arXiv:gr-qc/9902083] (which
relates two BD theory with different coupling) admitted by BD theory with scale
invariant matter content i.e $T^{\mu}{}_{\mu}=0$. Classically, this prohibits
the BD theory to reduce to General Relativity (GR) for scale invariant matter
content. We show that strong coupling limit of BD and GR both preserves the
symmetry involving scale factor. We also show that with a scale invariant
matter content (radiation i.e $P=\frac{1}{3}\rho$), the quantized BD theory
does reduce to GR as $\omega\rightarrow\infty$, which is in sharp contrast to
classical behavior. This is a first known illustration of a scenario, where
quantized BD theory provides example of anomalous symmetry breaking and
resulting binary phase structure. We make a conjecture regarding strong
coupling limit of BD theory in generic scenario.


title:
Time-resolved optical/near-IR polarimetry of V404 Cyg during its 2015
  outburst

abstract:
  We present optical and near-IR linear polarimetry of V404 Cyg during its 2015
outburst and in quiescence. We obtained time resolved r'-band polarimetry when
the source was in outburst, near-IR polarimetry when the source was near
quiescence and multiple wave-band optical polarimetry later in quiescence. The
optical to near-IR linear polarization spectrum can be described by
interstellar dust and an intrinsic variable component. The intrinsic optical
polarization, detected during the rise of one of the brightest flares of the
outburst, is variable, peaking at 4.5 per cent and decaying to 3.5 per cent. We
present several arguments that favour a synchrotron jet origin to this variable
polarization, with the optical emission originating close to the jet base. The
polarization flare occurs during the initial rise of a major radio flare event
that peaks later, and is consistent with a classically evolving synchrotron
flare from an ejection event. We conclude that the optical polarization flare
represents a jet launching event; the birth of a major ejection. For this event
we measure a rather stable polarization position angle of -9 degrees E of N,
implying that the magnetic field near the base of the jet is approximately
perpendicular to the jet axis. This may be due to the compression of magnetic
field lines in shocks in the accelerated plasma, resulting in a partially
ordered transverse field that have now been seen during the 2015 outburst. We
also find that this ejection occurred at a similar stage in the repetitive
cycles of flares.


title: Polarized synchrotron emission in quiescent black hole X-ray transients

abstract:
  We present near-infrared polarimetric observations of the black hole X-ray
binaries Swift J1357.2-0933 and A0620-00. In both sources, recent studies have
demonstrated the presence of variable infrared synchrotron emission in
quiescence, most likely from weak compact jets. For Swift J1357.2-0933 we find
that the synchrotron emission is polarized at a level of 8.0 +- 2.5 per cent (a
3.2 sigma detection of intrinsic polarization). The mean magnitude and rms
variability of the flux (fractional rms of 19-24 per cent in K_s-band) agree
with previous observations. These properties imply a continuously launched
(stable on long timescales), highly variable (on short timescales) jet in the
Swift J1357.2-0933 system in quiescence, which has a moderately tangled
magnetic field close to the base of the jet. We find that for A0620-00, there
are likely to be three components to the optical-infrared polarization;
interstellar dust along the line of sight, scattering within the system, and an
additional source that changes the polarization position angle in the reddest
(H and K_s) wave-bands. We interpret this as a stronger contribution of
synchrotron emission, and by subtracting the line-of-sight polarization, we
measure an excess of ~ 1.25 +- 0.28 per cent polarization and a position angle
of the magnetic field vector that is consistent with being parallel with the
axis of the resolved radio jet. These results imply that weak jets in low
luminosity accreting systems have magnetic fields which possess similarly
tangled fields compared to the more luminous, hard state jets in X-ray
binaries.


title: Urban Pulse: Capturing the Rhythm of Cities

abstract:
  Cities are inherently dynamic. Interesting patterns of behavior typically
manifest at several key areas of a city over multiple temporal resolutions.
Studying these patterns can greatly help a variety of experts ranging from city
planners and architects to human behavioral experts. Recent technological
innovations have enabled the collection of enormous amounts of data that can
help in these studies. However, techniques using these data sets typically
focus on understanding the data in the context of the city, thus failing to
capture the dynamic aspects of the city. The goal of this work is to instead
understand the city in the context of multiple urban data sets. To do so, we
define the concept of an "urban pulse" which captures the spatio-temporal
activity in a city across multiple temporal resolutions. The prominent pulses
in a city are obtained using the topology of the data sets, and are
characterized as a set of beats. The beats are then used to analyze and compare
different pulses. We also design a visual exploration framework that allows
users to explore the pulses within and across multiple cities under different
conditions. Finally, we present three case studies carried out by experts from
two different domains that demonstrate the utility of our framework.

categories: cs.CY cs.GR cs.SI physics.data-an physics.soc-ph


title: Quantum Entanglement Growth Under Random Unitary Dynamics

abstract:
  Characterizing how entanglement grows with time in a many-body system, for
example after a quantum quench, is a key problem in non-equilibrium quantum
physics. We study this problem for the case of random unitary dynamics,
representing either Hamiltonian evolution with time--dependent noise or
evolution by a random quantum circuit. Our results reveal a universal structure
behind noisy entanglement growth, and also provide simple new heuristics for
the `entanglement tsunami' in Hamiltonian systems without noise. In 1D, we show
that noise causes the entanglement entropy across a cut to grow according to
the celebrated Kardar--Parisi--Zhang (KPZ) equation. The mean entanglement
grows linearly in time, while fluctuations grow like $(\text{time})^{1/3}$ and
are spatially correlated over a distance $\propto (\text{time})^{2/3}$. We
derive KPZ universal behaviour in three complementary ways, by mapping random
entanglement growth to: (i) a stochastic model of a growing surface; (ii) a
`minimal cut' picture, reminiscent of the Ryu--Takayanagi formula in
holography; and (iii) a hydrodynamic problem involving the dynamical spreading
of operators. We demonstrate KPZ universality in 1D numerically using
simulations of random unitary circuits. Importantly, the leading order time
dependence of the entropy is deterministic even in the presence of noise,
allowing us to propose a simple `minimal cut' picture for the entanglement
growth of generic Hamiltonians, even without noise, in arbitrary
dimensionality. We clarify the meaning of the `velocity' of entanglement growth
in the 1D `entanglement tsunami'. We show that in higher dimensions, noisy
entanglement evolution maps to the well-studied problem of pinning of a
membrane or domain wall by disorder.

categories: cond-mat.stat-mech cond-mat.str-el hep-th quant-ph


title: The Weak Gravity Conjecture and Effective Field Theory

abstract:
  The Weak Gravity Conjecture (WGC) is a proposed constraint on theories with
gauge fields and gravity, requiring the existence of light charged particles
and/or imposing an upper bound on the field theory cutoff $\Lambda$. If taken
as a consistency requirement for effective field theories (EFTs), it rules out
possibilities for model-building including some models of inflation. I
demonstrate simple models which satisfy all forms of the WGC, but which through
Higgsing of the original gauge fields produce low-energy EFTs with gauge forces
that badly violate the WGC. These models illustrate specific loopholes in
arguments that motivate the WGC from a bottom-up perspective; for example the
arguments based on magnetic monopoles are evaded when the magnetic confinement
that occurs in a Higgs phase is accounted for. This indicates that the WGC
should not be taken as a veto on EFTs, even if it turns out to be a robust
property of UV quantum gravity theories. However, if the latter is true then
parametric violation of the WGC at low energy comes at the cost of non-minimal
field content in the UV. I propose that only a very weak constraint is
applicable to EFTs, $\Lambda \lesssim \left(-\log g \right)^{-1/2} M_\text{pl}$
where $g$ is the gauge coupling, motivated by entropy bounds. Remarkably, EFTs
produced by Higgsing a theory that satisfies the WGC can saturate but not
violate this bound.


title: A novel approach for identifying host galaxies of nearby FRBs

abstract:
  We report on a search for host galaxies of a subset of Rotating Radio
Transients (RRATs) that possess a dispersion measure (DM) near or above the
maximum Galactic value in their direction. These RRATs could have an
extragalactic origin and therefore be Fast Radio Bursts (FRBs). The sizes of
related galaxies on the sky at such short distances are comparable to the beam
size of a single-dish telescope (for example, the $7.0'$ radius of the Parkes
beam). Hence the association, if found, could be more definitive as compared to
finding host galaxies for more distant FRBs. We did not find any host galaxy
associated with six RRATs near the maximum Galactic DM. This result is
consistent with the fact that the probability of finding an FRB host galaxy
within this volume is also very small. We propose that future follow-up
observations of such RRATs be carried out in searching for local host galaxies
as well as the sources of FRBs.


title: Norms of random matrices: local and global problems

abstract:
  Can the behavior of a random matrix be improved by modifying a small fraction
of its entries? Consider a random matrix $A$ with i.i.d. entries. We show that
the operator norm of $A$ can be reduced to the optimal order $O(\sqrt{n})$ by
zeroing out a small submatrix of $A$ if and only if the entries have zero mean
and finite variance. Moreover, we obtain an almost optimal dependence between
the size of the removed submatrix and the resulting operator norm. Our approach
utilizes the cut norm and Grothendieck-Pietsch factorization for matrices, and
it combines the methods developed recently by C. Le and R. Vershynin and by E.
Rebrova and K. Tikhomirov.


title:
State Duration and Interval Modeling in Hidden Semi-Markov Model for
  Sequential Data Analysis

abstract:
  Sequential data modeling and analysis have become indispensable tools for
analyzing sequential data, such as time-series data, because larger amounts of
sensed event data have become available. These methods capture the sequential
structure of data of interest, such as input-output relations and correlation
among datasets. However, because most studies in this area are specialized or
limited to their respective applications, rigorous requirement analysis of such
models has not been undertaken from a general perspective. Therefore, we
particularly examine the structure of sequential data, and extract the
necessity of `state duration' and `state interval' of events for efficient and
rich representation of sequential data. Specifically addressing the hidden
semi-Markov model (HSMM) that represents such state duration inside a model, we
attempt to add representational capability of a state interval of events onto
HSMM. To this end, we propose two extended models: an interval state hidden
semi-Markov model (IS-HSMM) to express the length of a state interval with a
special state node designated as "interval state node"; and an interval length
probability hidden semi-Markov model (ILP-HSMM) which represents the length of
the state interval with a new probabilistic parameter "interval length
probability." Exhaustive simulations have revealed superior performance of the
proposed models in comparison with HSMM. These proposed models are the first
reported extensions of HMM to support state interval representation as well as
state duration representation.


title: New Horizons Constraints on Charon's Present Day Atmosphere

abstract:
  We report on a variety of standard techniques used by New Horizons including
a solar ultraviolet occultation, ultraviolet airglow observations, and
high-phase look-back particulate search imaging to search for an atmosphere
around Pluto's large moon Charon during its flyby in July 2015. Analyzing these
datasets, no evidence for a present day atmosphere has been found for 14
potential atomic and molecular species, all of which are now constrained to
have pressures below 0.3 nanobar, as we describe below, these are much more
stringent upper limits than the previously available 15-110 nanobar constraints
(e.g., Sicardy et al. 2006); for example, we find a 3$\sigma$ upper limit for
an N$_2$ atmosphere on Charon is 4.2 picobars and a 3$\sigma$ upper limit for
the brightness of any atmospheric haze on Charon of I/F=2.6x10$^{-5}$. A radio
occultation search for an atmosphere around Charon was also conducted by New
Horizons but will be published separately by other authors.


title: An Approximate Nerve Theorem

abstract:
  The Nerve Theorem relates the topological type of a suitably nice space with
the nerve of a good cover of that space. It has many variants, such as to
consider acyclic covers and numerous applications in topology including applied
and computational topology. The goal of this paper is to relax the notion of a
good cover to an approximately good cover, or more precisely, we introduce the
notion of an $\varepsilon$-acyclic cover. We use persistent homology to make
this rigorous and prove tight bounds between the persistent homology of a space
endowed with a function and the persistent homology of the nerve of an
$\varepsilon$-acyclic cover of the space. Using the Mayer-Vietoris spectral
sequence, we upper bound how local non-acyclicity can affect the global
homology. To prove the best possible bound we must introduce special cases of
interleavings between persistence modules called left and right interleavings.
Finally, we provide examples which achieve the bound proving the lower bound
and tightness of the result.


title:
The Lost Dwarfs of Centaurus A and the Formation of its Dark Globular
  Clusters

abstract:
  We present theoretical constraints for the formation of the newly discovered
dark star clusters (DSCs) with high mass-to-light (M/L) ratios, from Taylor et
al (2015). These compact stellar systems photometrically resemble globular
clusters (GCs) but have dynamical M/L ratios of ~ 10 - 100, closer to the
expectations for dwarf galaxies. The baryonic properties of the dark star
clusters (DSCs) suggest their host dark matter halos likely virialized at high
redshift with M > 10^8 M_sun. We use a new set of high-resolution N-body
simulations of Centaurus A to determine if there is a set of z=0 subhalos whose
properties are in line with these observations. While we find such a set of
subhalos, when we extrapolate the dark matter density profiles into the inner
20 pc, no dark matter halo associated with Centaurus A in our simulations, at
any redshift, can replicate the extremely high central mass densities of the
DSCs. Among the most likely options for explaining 10^5 - 10^7 M_sun within 10
pc diameter subhalos is the presence of a central massive black hole. We,
therefore, propose that the DSCs are remnant cusps of stellar systems
surrounding the central black holes of dwarf galaxies which have been almost
completely destroyed by interactions with Centaurus A.


title: Isotone projection cones and Q-matrices

abstract:
  Proper cones with the property that the projection onto them is isotone with
respect to the order they induce are called isotone projection cones. Isotone
projection cones and their extensions have been used to solve complementarity
problems and variational inequalities. Q-matrices are matrices with the
property that all classical linear complementarity problems defined by them are
solvable. This note will use the isotone projection cones to generate a large
class of Q-matrices. More specifically, it will be shown that the product
between a non-negative matrix with positive diagonal elements and a Stieltjes
matrix is a Q-matrix.


title:
Strategic Growth with Recursive Preferences: Decreasing Marginal
  Impatience

abstract:
  We study the interaction between strategy, heterogeneity and growth in a
two-agent model of capital accumulation. Preferences are represented by
recursive utility functions with decreasing marginal impatience. The stationary
equilibria of this dynamic game are analyzed under two alternative information
structures: one in which agents precommit to future actions, and another one
where agents use Markovian strategies. In both cases, we develop sufficient
conditions to prove the existence of equilibria and characterize their
stability properties. The precommitment case is characterized by monotone
convergence, but Markovian equilibria may exhibit nonmonotonic paths, even in
the long-run.


title:
A wind-driving disc model for the mm-wavelength polarization structure
  of HL Tau

abstract:
  The recent advent of spatially resolved mm- and cm-wavelength polarimetry in
protostellar accretion discs could help clarify the role of magnetic fields in
the angular momentum transport in these systems. The best case to date is that
of HL~Tau, where the inability to produce a good fit to the 1.25-mm data with a
combination of vertical and azimuthal magnetic field components was interpreted
as implying that centrifugally driven winds (CDWs) are probably not a
significant transport mechanism on the $\sim 10^2\,$au scale probed by the
observations. Using synthetic polarization maps of heuristic
single-field-component discs and of a post-processed simulation of a
wind-driving disc, we demonstrate that a much better fit to the data can be
obtained if the radial field component, a hallmark of the CDW mechanism,
dominates in the polarized emission region. A similar inference was previously
made in modelling the far-infrared polarization map of the pc-scale dust ring
in the Galactic centre. To reconcile this interpretation with theoretical
models of protostellar discs, which indicate that the wind is launched from a
comparatively high elevation above the mid-plane, we propose that most of the
polarized emission originates -- with a high ($\ga 10$\%) intrinsic degree of
polarization -- in small ($\la 0.1\,$mm) grains that remain suspended above the
mid-plane, and that the bulk of the mm-wavelength emission is produced -- with
low intrinsic polarization -- by larger grains that have settled to the
mid-plane.


title: Enclosings of Decompositions of Complete Multigraphs in 2-Factorizations

abstract:
  Let $k$, $\lambda$ and $\mu$ be positive integers. A decomposition of a
multigraph $ \lambda G$ into edge-disjoint subgraphs $G_1, \ldots , G_k$ is
said to be \emph{enclosed} by a decomposition of a multigraph $\mu H$ into
edge-disjoint subgraphs $H_1, \ldots , H_k$ if $\mu > \lambda$ and $G_i$ is a
subgraph of $H_i$, $1 \leq i \leq k$. In this paper we initiate the study of
when a decomposition can be enclosed by a decomposition that consists of
spanning subgraphs.
  A decomposition of a graph is a 2-factorization if each subgraph is 2-regular
and is Hamiltonian if each subgraph is a Hamiltonian cycle. Let $n$ and $m$ be
positive integers. We give necessary and sufficient conditions for enclosing a
decomposition of $\lambda K_n$ in a $2$-factorization of $\mu K_{n+m}$ whenever
$\mu>\lambda$ and $m \geq n-2$. We also give necessary and sufficient
conditions for enclosing a decomposition of $\lambda K_n$ in a Hamiltonian
decomposition of $\mu K_{n+m}$ whenever $\mu > \lambda$ and $m \geq n-1$, or
$\mu > \lambda$, $n=3$ and $m=1$, or $\mu = 2$, $\lambda=1$ and $m=n-2$.


title: Silicon nanophotonics for scalable quantum coherent feedback networks

abstract:
  The emergence of coherent quantum feedback control (CQFC) as a new paradigm
for precise manipulation of dynamics of complex quantum systems has led to the
development of efficient theoretical modeling and simulation tools and opened
avenues for new practical implementations. This work explores the applicability
of the integrated silicon photonics platform for implementing scalable CQFC
networks. If proven successful, on-chip implementations of these networks would
provide scalable and efficient nanophotonic components for autonomous quantum
information processing devices and ultra-low-power optical processing systems
at telecommunications wavelengths. We analyze the strengths of the silicon
photonics platform for CQFC applications and identify the key challenges to
both the theoretical formalism and experimental implementations. In particular,
we determine specific extensions to the theoretical CQFC framework (which was
originally developed with bulk-optics implementations in mind), required to
make it fully applicable to modeling of linear and nonlinear integrated optics
networks. We also report the results of a preliminary experiment that studied
the performance of an in situ controllable silicon nanophotonic network of two
coupled cavities and analyze the properties of this device using the CQFC
formalism.


title:
Experimental Preparation of Topologically Ordered States via Adiabatic
  Evolution

abstract:
  Topological orders are a class of exotic states of matter characterized by
patterns of long-range entanglement. Certain topologically ordered systems are
proposed as potential realization of fault-tolerant quantum computation.
Topological orders can arise in two-dimensional spin-lattice models. In this
paper, we engineer a time-dependent Hamiltonian to prepare a topologically
ordered state through adiabatic evolution. The other sectors in the degenerate
ground-state space of the model are obtained by applying nontrivial operations
corresponding to closed string operators. Each sector is highly entangled, as
shown from the completely reconstructed density matrices. This paves the way
towards exploring the properties of topological orders and the application of
topological orders in topological quantum memory.


title: Constraints on Large Extra Dimensions from the MINOS Experiment

abstract:
  We report new constraints on the size of large extra dimensions from data
collected by the MINOS experiment between 2005 and 2012. Our analysis employs a
model in which sterile neutrinos arise as Kaluza-Klein states in large extra
dimensions and thus modify the neutrino oscillation probabilities due to mixing
between active and sterile neutrino states. Using Fermilab's NuMI beam exposure
of $10.56 \times 10^{20}$ protons-on-target, we combine muon neutrino charged
current and neutral current data sets from the Near and Far Detectors and
observe no evidence for deviations from standard three-flavor neutrino
oscillations. The ratios of reconstructed energy spectra in the two detectors
constrain the size of large extra dimensions to be smaller than
$0.45\,\mu\text{m}$ at 90% C.L. in the limit of a vanishing lightest active
neutrino mass. Stronger limits are obtained for non-vanishing masses.


title: Derived intersections over the Hochschild cochain complex

abstract:
  The paper generalizes a result of Behrend-Fantechi and Baranovsky-Ginzburg to
the 1-shifted cotangent bundle $T^*X[1]$ of a smooth scheme $X$ over the field
of complex numbers. We show how one can obtain twisted cotangent bundles as
derived intersections of Lagrangians in $T^*X[1]$, moreover and we show that
the derived intersection of the quantized Lagrangians coincide with the
canonical quantization of the twisted cotangent bundles.


title:
Dynamics of small trapped one-dimensional Fermi gas under oscillating
  magnetic fields

abstract:
  Deterministic preparation of an ultracold harmonically trapped
one-dimensional Fermi gas consisting of a few fermions has been realized by the
Heidelberg group. Using Floquet formalism, we study the time dynamics of two-
and three-fermion systems in a harmonic trap under an oscillating magnetic
field. The oscillating magnetic field produces a time-dependent interaction
strength through a Feshbach resonance. We explore the dependence of these
dynamics on the frequency of the oscillating magnetic field for
non-interacting, weakly interacting, and strongly interacting systems. We
identify the regimes where the system can be described by an effective
two-state model and an effective three-state model. We find an unbounded
coupling to all excited states at the infinitely strong interaction limit and
several simple relations that characterize the dynamics. Based on our findings,
we propose a technique for driving transition from the ground state to the
excited states using an oscillating magnetic field.


title:
An elementary proof of Bevan's theorem on the growth of grid classes of
  permutations

abstract:
  Bevan established that the growth rate of a monotone grid class of
permutations is equal to the square of the spectral radius of a related
bipartite graph. We give an elementary and self-contained proof of a
generalization of this result using only Stirling's Formula, the method of
Lagrange multipliers, and the singular value decomposition of matrices.


title: Local limits of Markov Branching trees and their volume growth

abstract:
  We are interested in the local limits of families of random trees that
satisfy the Markov branching property, which is fulfilled by a wide range of
models. Loosely, this property entails that given the sizes of the sub-trees
above the root, these sub-trees are independent and their distributions only
depend upon their respective sizes. The laws of the elements of a Markov
branching family are characterised by a sequence of probability distributions
on the sets of integer partitions which describes how the sizes of the
sub-trees above the root are distributed.
  We prove that under some natural assumption on this sequence of
probabilities, when their sizes go to infinity, the trees converge in
distribution to an infinite tree which also satisfies the Markov branching
property. Furthermore, when this infinite tree has a single path from the root
to infinity, we give conditions to ensure its convergence in distribution under
appropriate rescaling of its distance and counting measure to a self-similar
fragmentation tree with immigration. In particular, this allows us to determine
how, in this infinite tree, the "volume" of the ball of radius $R$ centred at
the root asymptotically grows with $R$.
  Our unified approach will allow us to develop various new applications, in
particular to different models of growing trees and cut-trees, and to recover
known results. An illustrative example lies in the study of Galton-Watson
trees: the distribution of a critical Galton-Watson tree conditioned on its
size converges to that of Kesten's tree when the size grows to infinity. If
furthermore, the offspring distribution has finite variance, under adequate
rescaling, Kesten's tree converges to Aldous' self-similar CRT and the total
size of the $R$ first generations asymptotically behaves like $R^2$.


title: On the growth of merges and staircases of permutation classes

abstract:
  There is a well-known upper bound on the growth rate of the merge of two
permutation classes. Curiously, there is no known merge for which this bound is
not achieved. Using staircases of permutation classes, we provide sufficient
conditions for this upper bound to be achieved. In particular, our results
apply to all merges of principal permutation classes. We end by demonstrating
how our techniques can be used to reprove a result of B\'ona.


title: White holes in Einstein-aether theory

abstract:
  We perform numerical simulations of gravitational collapse in Einstein-aether
theory. We find that under certain conditions, the collapse results in the
temporary formation of a white hole horizon.


title: Protein Collapse is Encoded in the Folded State Architecture

abstract:
  Natural protein sequences that self-assemble to form globular structures are
compact with high packing densities in the folded states. It is known that
proteins unfold upon addition of denaturants, adopting random coil structures.
The dependence of the radii of gyration on protein size in the folded and
unfolded states obeys the same scaling laws as synthetic polymers. Thus, one
might surmise that the mechanism of collapse in proteins and polymers ought to
be similar. However, because the number of amino acids in single domain
proteins is not significantly greater than about two hundred, it has not been
resolved if the unfolded states of proteins are compact under conditions that
favor the folded states - a problem at the heart of how proteins fold. By
adopting a theory used to derive polymer-scaling laws, we find that the
propensity for the unfolded state of a protein to be compact is universal and
is encoded in the contact map of the folded state. Remarkably, analysis of over
2000 proteins shows that proteins rich in $\beta$-sheets have greater tendency
to be compact than $\alpha$-helical proteins. The theory provides insights into
the reasons for the small size of single domain proteins and the physical basis
for the origin of multi-domain proteins. Application to non-coding RNA
molecules show that they have evolved to collapse sharing similarities to
$\beta$-sheet proteins. An implication of our theory is that the evolution of
natural foldable sequences is guided by the requirement that for efficient
folding they should populate minimum energy compact states under folding
conditions. This concept also supports the compaction selection hypothesis used
to rationalize the unusually condensed states of viral RNA molecules.

categories: q-bio.BM cond-mat.soft cond-mat.stat-mech physics.bio-ph


title:
Design-Space Exploration and Optimization of an Energy-Efficient and
  Reliable 3D Small-world Network-on-Chip

abstract:
  A three-dimensional (3D) Network-on-Chip (NoC) enables the design of high
performance and low power many-core chips. Existing 3D NoCs are inadequate for
meeting the ever-increasing performance requirements of many-core processors
since they are simple extensions of regular 2D architectures and they do not
fully exploit the advantages provided by 3D integration. Moreover, the
anticipated performance gain of a 3D NoC-enabled many-core chip may be
compromised due to the potential failures of through-silicon-vias (TSVs) that
are predominantly used as vertical interconnects in a 3D IC. To address these
problems, we propose a machine-learning-inspired predictive design methodology
for energy-efficient and reliable many-core architectures enabled by 3D
integration. We demonstrate that a small-world network-based 3D NoC (3D SWNoC)
performs significantly better than its 3D MESH-based counterparts. On average,
the 3D SWNoC shows 35% energy-delay-product (EDP) improvement over 3D MESH for
the PARSEC and SPLASH2 benchmarks considered in this work. To improve the
reliability of 3D NoC, we propose a computationally efficient spare-vertical
link (sVL) allocation algorithm based on a state-space search formulation. Our
results show that the proposed sVL allocation algorithm can significantly
improve the reliability as well as the lifetime of 3D SWNoC.


title:
Millihertz quasi-periodic oscillations in 4U 1636-53 associated with
  bursts with positive convexity only

abstract:
  We investigated the convexity of all type I X-ray bursts with millihertz
quasi-periodic oscillations (mHz QPOs) in 4U 1636-53 using archival
observations with the Rossi X-ray Timing Explorer. We found that, at a 3.5
$\sigma$ confidence level, in all 39 cases in which the mHz QPOs disappeared at
the time of an X-ray burst, the convexity of the burst is positive. The
convexity measures the shape of the rising part of the burst light curve and,
according to recent models, it is related to the ignition site of bursts on the
neutron star surface. This finding suggests that in 4U 1636-53 these 39 bursts
and the marginally-stable nuclear burning process responsible for the mHz QPOs
take place at the neutron-star equator. This scenario could explain the
inconsistency between the high accretion rate required for triggering mHz QPOs
in theoretical models and the relatively low accretion rate derived from
observations.


title:
Low Rank Alternating Direction Method of Multipliers Reconstruction for
  MR Fingerprinting

abstract:
  Purpose
  The proposed reconstruction framework addresses the reconstruction accuracy,
noise propagation and computation time for Magnetic Resonance Fingerprinting
(MRF).
  Methods
  Based on a singular value decomposition (SVD) of the signal evolution, MRF is
formulated as a low rank inverse problem in which one image is reconstructed
for each singular value under consideration. This low rank approximation of the
signal evolution reduces the computational burden by reducing the number of
Fourier transformations. Also, the low rank approximation improves the
conditioning of the problem, which is further improved by extending the low
rank inverse problem to an augmented Lagrangian that is solved by the
alternating direction method of multipliers (ADMM). The root mean square error
and the noise propagation are analyzed in simulations. For verification, in
vivo examples are provided.
  Results
  The proposed low rank ADMM approach shows a reduced root mean square error
compared to the original fingerprinting reconstruction, to a low rank
approximation alone and to an ADMM approach without a low rank approximation.
Incorporating sensitivity encoding allows for further artifact reduction.
  Conclusion
  The proposed reconstruction provides robust convergence, reduced
computational burden and improved image quality compared to other MRF
reconstruction approaches evaluated in this study.


title:
N\'eel walls with prescribed winding number and how a nonlocal term can
  change the energy landscape

abstract:
  We study a nonlocal Allen-Cahn type problem for vector fields of unit length,
arising from a model for domain walls (called N\'eel walls) in ferromagnetism.
We show that the nonlocal term gives rise to new features in the energy
landscape; in particular, we prove existence of energy minimisers with
prescribed winding number that would be prohibited in a local model.


title:
Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials with applications to
  series involving zeros of Bessel functions

abstract:
  We introduce Bernoulli-Dunkl and Apostol-Euler-Dunkl polynomials as
generalizations of Bernoulli and Apostol-Euler polynomials, where the role of
the derivative is now played by the Dunkl operator on the real line. We use
them to sum a bunch of series involving the zeros of Bessel functions.


title:
Eigenvalues and eigenvectors of heavy-tailed sample covariance matrices
  with general growth rates: the iid case

abstract:
  In this paper we study the joint distributional convergence of the largest
eigenvalues of the sample covariance matrix of a $p$-dimensional time series
with iid entries when $p$ converges to infinity together with the sample size
$n$. We consider only heavy-tailed time series in the sense that the entries
satisfy some regular variation condition which ensures that their fourth moment
is infinite. In this case, Soshnikov [31, 32] and Auffinger et al. [2] proved
the weak convergence of the point processes of the normalized eigenvalues of
the sample covariance matrix towards an inhomogeneous Poisson process which
implies in turn that the largest eigenvalue converges in distribution to a
Fr\'echet distributed random variable. They proved these results under the
assumption that $p$ and $n$ are proportional to each other. In this paper we
show that the aforementioned results remain valid if $p$ grows at any
polynomial rate. The proofs are different from those in [2, 31, 32]; we employ
large deviation techniques to achieve them. The proofs reveal that only the
diagonal of the sample covariance matrix is relevant for the asymptotic
behavior of the largest eigenvalues and the corresponding eigenvectors which
are close to the canonical basis vectors. We also discuss extensions of the
results to sample autocovariance matrices.


title:
Experimentally Probing Topological Order and Its Breakdown via Modular
  Matrices

abstract:
  The modern conception of phases of matter has undergone tremendous
developments since the first observation of topologically ordered states in
fractional quantum Hall systems in the 1980s. In this paper, we explore the
question: How much detail of the physics of topological orders can in principle
be observed using state of the art technologies? We find that using
surprisingly little data, namely the toric code Hamiltonian in the presence of
generic disorders and detuning from its exactly solvable point, the modular
matrices -- characterizing anyonic statistics that are some of the most
fundamental finger prints of topological orders -- can be reconstructed with
very good accuracy solely by experimental means. This is a first experimental
realization of these fundamental signatures of a topological order, a test of
their robustness against perturbations, and a proof of principle -- that
current technologies have attained the precision to identify phases of matter
and, as such, probe an extended region of phase space around the soluble point
before its breakdown. Given the special role of anyonic statistics in quantum
computation, our work promises myriad applications both in probing and
realistically harnessing these exotic phases of matter.


title:
Remarks on the effects of the Gribov copies on the infrared behavior of
  higher dimensional Yang-Mills theory

abstract:
  In this paper, we discuss non-perturbative infrared features of Yang-Mills
theory in Euclidean space-time dimensions greater than four in the Landau gauge
and within the Refined Gribov-Zwanziger framework, which enables us to take
into account the existence of gauge copies by restricting the domain of
integration in the path integral to the Gribov region. Evidences for a
decoupling/massive solution for the gluon propagator in higher dimensions are
provided. This behavior is strengthened the bigger the dimension is. Further,
we show that, by a dimensional reduction of the Refined Gribov-Zwanziger action
from five to four dimensions, a non-perturbative coupling between the inverse
of the Faddeev-Popov operator and the scalar field corresponding to the fifth
component of the gauge field naturally arises, being in agreement with the
recently proposed mechanism \cite{Capri:2014bsa} to generalize the Refined
Gribov-Zwanziger construction to the matter sector.


title: A $\widetilde{O}(n)$ Non-Adaptive Tester for Unateness

abstract:
  Khot and Shinkar (RANDOM, 2016) recently describe an adaptive, $O(n
\log(n)/\varepsilon)$-query tester for unateness of Boolean functions
$f:\{0,1\}^n \to \{0,1\}$. In this note we describe a simple non-adaptive, $O(n
\log(n/\varepsilon)/\varepsilon)$ -query tester for unateness for functions
over the hypercube with any ordered range.


title: Orientations of graphs with uncountable chromatic number

abstract:
  Motivated by an old conjecture of P. Erd\H{o}s and V. Neumann-Lara, our aim
is to investigate digraphs with uncountable dichromatic number and orientations
of undirected graphs with uncountable chromatic number. A graph has uncountable
chromatic number if its vertices cannot be covered by countably many
independent sets, and a digraph has uncountable dichromatic number if its
vertices cannot be covered by countably many acyclic sets. We prove that
consistently there are digraphs with uncountable dichromatic number and
arbitrarily large digirth; this is in surprising contrast with the undirected
case: any graph with uncountable chromatic number contains a 4-cycle. Next, we
prove that several well known graphs (uncountable complete graphs, certain
comparability graphs, and shift graphs) admit orientations with uncountable
dichromatic number in ZFC. However, we show that the statement "every graph $G$
of size and chromatic number $\omega_1$ has an orientation $D$ with uncountable
dichromatic number" is independent of ZFC.


title: Small inertia regularization of an anisotropic aggregation model

abstract:
  We consider an anisotropic first-order ODE aggregation model and its
approximation by a second-order relaxation system. The relaxation model
contains a small parameter $\varepsilon$, which can be interpreted as inertia
or response time. We examine rigorously the limit $\varepsilon \to 0$ of
solutions to the relaxation system. Of major interest is how discontinuous (in
velocities) solutions to the first-order model are captured in the zero-inertia
limit. We find that near such discontinuities, solutions to the second-order
model perform fast transitions within a time layer of size
$\mathcal{O}(\varepsilon^{2/3})$. We validate this scale with numerical
simulations.


title: Macroscopic transport of a current-induced spin polarization

abstract:
  Experimental studies of spin transport in a two-dimensional electron gas
hosted by a triple GaAs/AlGaAs quantum well are reported. Using time-resolved
Kerr rotation, we observed the precession of the spin polarization about a
current-controlled spin-orbit magnetic field. Spatially-resolved imaging showed
a large variation of the electron g-factor and the drift transport of coherent
electron spins over distances exceeding half-millimetre in a direction
transverse to the electric field.


title: Learning an Optimization Algorithm through Human Design Iterations

abstract:
  Solving optimal design problems through crowdsourcing faces a dilemma: On one
hand, human beings have been shown to be more effective than algorithms at
searching for good solutions of certain real-world problems with
high-dimensional or discrete solution spaces; on the other hand, the cost of
setting up crowdsourcing environments, the uncertainty in the crowd's
domain-specific competence, and the lack of commitment of the crowd, all
contribute to the lack of real-world application of design crowdsourcing. We
are thus motivated to investigate a solution-searching mechanism where an
optimization algorithm is tuned based on human demonstrations on solution
searching, so that the search can be continued after human participants abandon
the problem. To do so, we model the iterative search process as a Bayesian
Optimization (BO) algorithm, and propose an inverse BO (IBO) algorithm to find
the maximum likelihood estimators of the BO parameters based on human
solutions. We show through a vehicle design and control problem that the search
performance of BO can be improved by recovering its parameters based on an
effective human search. Thus, IBO has the potential to improve the success rate
of design crowdsourcing activities, by requiring only good search strategies
instead of good solutions from the crowd.


title: A 4D Light-Field Dataset and CNN Architectures for Material Recognition

abstract:
  We introduce a new light-field dataset of materials, and take advantage of
the recent success of deep learning to perform material recognition on the 4D
light-field. Our dataset contains 12 material categories, each with 100 images
taken with a Lytro Illum, from which we extract about 30,000 patches in total.
To the best of our knowledge, this is the first mid-size dataset for
light-field images. Our main goal is to investigate whether the additional
information in a light-field (such as multiple sub-aperture views and
view-dependent reflectance effects) can aid material recognition. Since
recognition networks have not been trained on 4D images before, we propose and
compare several novel CNN architectures to train on light-field images. In our
experiments, the best performing CNN architecture achieves a 7% boost compared
with 2D image classification (70% to 77%). These results constitute important
baselines that can spur further research in the use of CNNs for light-field
applications. Upon publication, our dataset also enables other novel
applications of light-fields, including object detection, image segmentation
and view interpolation.


title:
A short review and primer on electrodermal activity in human computer
  interaction applications

abstract:
  The application of psychophysiology in human-computer interaction is a
growing field with significant potential for future smart personalised systems.
Working in this emerging field requires comprehension of an array of
physiological signals and analysis techniques.
  One of the most widely used signals is electrodermal activity, or EDA, also
known as galvanic skin response or GSR. This signal is commonly used as a proxy
for physiological arousal, but recent advances of interpretation and analysis
suggest that traditional approaches should be revised. We present a short
review on the application of EDA in human-computer interaction.
  This paper aims to serve as a primer for the novice, enabling rapid
familiarisation with the latest core concepts. We put special emphasis on
everyday human-computer interface applications to distinguish from the more
common clinical or sports uses of psychophysiology.
  This paper is an extract from a comprehensive review of the entire field of
ambulatory psychophysiology, including 12 similar chapters, plus application
guidelines and systematic review. Thus any citation should be made using the
following reference:
  B. Cowley, M. Filetti, K. Lukander, J. Torniainen, A. Henelius, L. Ahonen, O.
Barral, I. Kosunen, T. Valtonen, M. Huotilainen, N. Ravaja, G. Jacucci. The
Psychophysiology Primer: a guide to methods and a broad review with a focus on
human-computer interaction. Foundations and Trends in Human-Computer
Interaction, vol. 9, no. 3-4, pp. 150--307, 2016.


title: Silicate Composition of the Interstellar Medium

abstract:
  The composition of silicate dust in the diffuse interstellar medium and in
protoplanetary disks around young stars informs our understanding of the
processing and evolution of the dust grains leading up to planet formation.
Analysis of the well-known 9.7{\mu}m feature indicates that small amorphous
silicate grains represent a significant fraction of interstellar dust and are
also major components of protoplanetary disks. However, this feature is
typically modelled assuming amorphous silicate dust of olivine and pyroxene
stoichiometries. Here, we analyze interstellar dust with models of silicate
dust that include non-stoichiometric amorphous silicate grains. Modelling the
optical depth along lines of sight toward the extinguished objects Cyg OB2 No.
12 and {\zeta} Ophiuchi, we find evidence for interstellar amorphous silicate
dust with stoichiometry intermediate between olivine and pyroxene, which we
simply refer to as "polivene." Finally, we compare these results to models of
silicate emission from the Trapezium and protoplanetary disks in Taurus.


title: On nonsymmetric rank one singular perturbations of selfadjoint operators

abstract:
  We consider nonsymmetric rank one singular perturbations of a selfadjoint
operator, i.e., an expression of the form $\tilde A = A +
\alpha\left\langle\cdot, \omega_1\right\rangle\omega_2$, $\omega_1\not =
\omega_2$, $\alpha\in{\mathbb C}$, in a general case
$\omega_1,\omega_2\in{\mathcal H}_{-2}$. Using a constructive description of
the perturbed operator $\tilde A$, we investigate some spectral and
approximations properties of $\tilde A$. The wave operators corresponding to
the couple $A$, $\tilde A$ and a series of examples are also presented.


title: A better lower bound on average degree of k-list-critical graphs

abstract:
  We improve the best known bounds on average degree of $k$-list-critical
graphs for $k \ge 6$. Specifically, for $k \ge 7$ we show that every
non-complete $k$-list-critical graph has average degree at least $k-1 +
\frac{(k-3)^2 (2 k-3)}{k^4-2 k^3-11 k^2+28 k-14}$ and every non-complete
$6$-list-critical graph has average degree at least $5 + \frac{93}{766}$. The
same bounds hold for online $k$-list-critical graphs.


title: The Sharing Economy for the Smart Grid

abstract:
  The sharing economy has disrupted housing and transportation sectors.
Homeowners can rent out their property when they are away on vacation, car
owners can offer ride sharing services. These sharing economy business models
are based on monetizing under-utilized infrastructure. They are enabled by
peer-to-peer platforms that match eager sellers with willing buyers.
  Are there compelling sharing economy opportunities in the electricity sector?
What products or services can be shared in tomorrow's Smart Grid? We begin by
exploring sharing economy opportunities in the electricity sector, and discuss
regulatory and technical obstacles to these opportunities. We then study the
specific problem of a collection of firms sharing their electricity storage. We
characterize equilibrium prices for shared storage in a spot market. We
formulate storage investment decisions of the firms as a non-convex
non-cooperative game. We show that under a mild alignment condition, a Nash
equilibrium exists, it is unique, and it supports the social welfare. We
discuss technology platforms necessary for the physical exchange of power, and
market platforms necessary to trade electricity storage. We close with
synthetic examples to illustrate our ideas.


title: Gaussian hypothesis testing and quantum illumination

abstract:
  Quantum hypothesis testing is one of the most basic tasks in quantum
information theory and has fundamental links with quantum communication and
estimation theory. In this paper, we establish a formula that characterizes the
decay rate of the minimal Type-II error probability in a quantum hypothesis
test of two Gaussian states given a fixed constraint on the Type-I error
probability. This formula is a direct function of the mean vectors and
covariance matrices of the quantum Gaussian states in question. We give an
application to quantum illumination, which is the task of determining whether
there is a low-reflectivity object embedded in a target region with a bright
thermal-noise bath. For the asymmetric-error setting, we find that a quantum
illumination transmitter can achieve an error probability exponent stronger
than a coherent-state transmitter of the same mean photon number, and
furthermore, that it requires far fewer trials to do so. This occurs when the
background thermal noise is either low or bright, which means that a quantum
advantage is even easier to witness than in the symmetric-error setting because
it occurs for a larger range of parameters. Going forward from here, we expect
our formula to have applications in settings well beyond those considered in
this paper, especially to quantum communication tasks involving quantum
Gaussian channels.


title:
Tracing Slow Winds from T Tauri Stars via Low Velocity Forbidden Line
  Emission

abstract:
  Using Keck/HIRES spectra {\Delta}v ~ 7 km/s, we analyze forbidden lines of [O
I] 6300 {\AA}, [O I] 5577 {\AA} and [S II] 6731 {\AA} from 33 T Tauri stars
covering a range of disk evolutionary stages. After removing a high velocity
component (HVC) associated with microjets, we study the properties of the low
velocity component (LVC). The LVC can be attributed to slow disk winds that
could be magnetically (MHD) or thermally (photoevaporative) driven. Both of
these winds play an important role in the evolution and dispersal of
protoplanetary material.
  LVC emission is seen in all 30 stars with detected [O I] but only in 2 out of
eight with detected [S II] , so our analysis is largely based on the properties
of the [O I] LVC. The LVC itself is resolved into broad (BC) and narrow (NC)
kinematic components. Both components are found over a wide range of accretion
rates and their luminosity is correlated with the accretion luminosity, but the
NC is proportionately stronger than the BC in transition disks.
  The FWHM of both the BC and NC correlates with disk inclination, consistent
with Keplerian broadening from radii of 0.05 to 0.5 AU and 0.5 to 5 AU,
respectively. The velocity centroids of the BC suggest formation in an MHD disk
wind, with the largest blueshifts found in sources with closer to face-on
orientations. The velocity centroids of the NC however, show no dependence on
disk inclination. The origin of this component is less clear and the evidence
for photoevaporation is not conclusive.


title: Densely Connected Convolutional Networks

abstract:
  Recent work has shown that convolutional networks can be substantially
deeper, more accurate, and efficient to train if they contain shorter
connections between layers close to the input and those close to the output. In
this paper, we embrace this observation and introduce the Dense Convolutional
Network (DenseNet), which connects each layer to every other layer in a
feed-forward fashion. Whereas traditional convolutional networks with L layers
have L connections - one between each layer and its subsequent layer - our
network has L(L+1)/2 direct connections. For each layer, the feature-maps of
all preceding layers are used as inputs, and its own feature-maps are used as
inputs into all subsequent layers. DenseNets have several compelling
advantages: they alleviate the vanishing-gradient problem, strengthen feature
propagation, encourage feature reuse, and substantially reduce the number of
parameters. We evaluate our proposed architecture on four highly competitive
object recognition benchmark tasks (CIFAR-10, CIFAR-100, SVHN, and ImageNet).
DenseNets obtain significant improvements over the state-of-the-art on most of
them, whilst requiring less computation to achieve high performance. Code and
pre-trained models are available at https://github.com/liuzhuang13/DenseNet .


title: Learning About the Magnetar Swift J1834.9-0846 from its Wind Nebula

abstract:
  The first wind nebula around a magnetar was recently discovered in X-rays
around Swift~J1834.9$-$0846. We study this magnetar's global energetics and the
properties of its particle wind or outflows. At a distance of $\sim4\;$kpc,
Swift~J1834.9$-$0846 is located at the center of the supernova remnant (SNR)
W41 whose radius is $\sim 19\;$pc, an order of magnitude larger than that of
the X-ray nebula ($\sim2\;$pc). The association with SNR W41 suggests a common
age of $\sim5-100\;$kyr, while its spin-down age is $4.9$~kyr. A small natal
kick velocity may partly explain why a wind nebula was detected around this
magnetar but not around other magnetars, most of which appear to have larger
kick velocities and may have exited their birth SNR. We find that the GeV and
TeV source detected by Fermi/LAT and H.E.S.S., respectively, of radius
$\sim11\;$pc is most likely of hadronic origin. The dynamics and internal
structure of the nebula are examined analytically to explain the nebula's
current properties. Its size may naturally correspond to the
diffusion-dominated cooling length of the X-ray emitting $e^+e^-$ pairs. This
may also account for the spectral softening of the X-ray emission from the
nebula's inner to outer parts. Analysis of the X-ray synchrotron nebula implies
that (i) the nebular magnetic field is $\gtrsim 11\;\mu$G (and likely
$\lesssim30\;\mu$G), and (ii) the nebula is not powered predominantly by the
magnetar's quiescent spin-down-powered MHD wind, but by other outflows that
contribute most of its energy. The latter are most likely associated with the
magnetar's bursting activity, and possibly dominated by outflows associated
with its past giant flares. The energy source for the required outflows cannot
be the decay of the magnetar's dipole field alone, and is most likely the decay
of its much stronger internal magnetic field.


title:
Multi-phase Nature of a Radiation-Driven Fountain with Nuclear Starburst
  in a Low-mass Active Galactic Nucleus

abstract:
  The structures and dynamics of molecular, atomic, and ionized gases are
studied around a low-luminosity active galactic nucleus (AGN) with a small
($2\times 10^6 M_\odot$) black hole using 3D radiation hydrodynamic
simulations. We studied, for the first time, the non-equilibrium chemistry for
the X-ray dominated region in the "radiation-driven fountain" (Wada 2012) with
supernova feedback. A double hollow cone structure is naturally formed without
postulating a thick "torus" around a central source. The cone is occupied with
an inhomogeneous, diffuse ionized gas and surrounded by a geometrically thick
($h/r \gtrsim 1$) atomic gas. Dense molecular gases are distributed near the
equatorial plane, and energy feedback from supernovae enhances their scale
height. Molecular hydrogen exists in a hot phase ( > 1000 K) as well as in a
cold ( < 100 K), dense ( >$10^3$ cm$^{-3}$) phase. The velocity dispersion of
H$_2$ in the vertical direction is comparable to the rotational velocity, which
is consistent with near infrared observations of nearby Seyfert galaxies. Using
3D radiation transfer calculations for the dust emission, we find polar
emission in the mid-infrared band (12$\mu m$), which is associated with bipolar
outflows, as suggested in recent interferometric observations of nearby AGNs.
If the viewing angle for the nucleus is larger than 75 deg, the spectral energy
distribution (~ 2 -- 60 $\mu m$) of this model is consistent with that of the
Circinus galaxy. The multi-phase interstellar medium observed in
optical/infrared and X-ray observations is also discussed.


title: A mis\`ere play $\star$-operator

abstract:
  We study the $\star$-operator (Larsson et al. 2011) of impartial vector
subtraction games (Golomb 1965). Here we extend the notion to the mis\`ere-play
convention, and prove convergence and other properties; notably more structure
is obtained under mis\`ere-play as compared with the normal-play convention
(Larsson 2012).


title: Two-dimensional Superconductors with Atomic-scale Thicknesses

abstract:
  Recent progress in two-dimensional superconductors with atomic-scale
thicknesses is reviewed mainly from the experimental point of view. The
superconducting systems treated here involve a variety of materials and forms:
elemental-metal ultrathin films and atomic layers on semiconductor surfaces;
interfaces and superlattices of heterostructures made of cuprates, perovskite
oxides, and rare-earth metal heavy-fermion compounds; interfaces of
electric-double-layer transistors; graphene and atomic sheets of
transition-metal dichalcogenide; iron selenide and organic conductors on oxide
and metal surfaces, respectively. Unique phenomena arising from the ultimate
two-dimensionality of the system and the physics behind them are discussed.


title: Maximum atom-bond connectivity index with given graph parameters

abstract:
  The atom-bond connectivity (ABC) index is a degree-based topological index.
It was introduced due to its applications in modeling the properties of certain
molecular structures and has been since extensively studied. In this note, we
examine the influence on the extremal values of the ABC index by various graph
parameters. More specifically, we consider the maximum ABC index of connected
graphs of given order, with fixed independence number, number of pendent
vertices, chromatic number and edge-connectivity respectively. We provide
characterizations of extremal structures as well as some conjectures. Numerical
analysis of the extremal values are also presented.


title: A Radiative Model of Quark Masses with Binary Tetrahedral Symmetry

abstract:
  A radiative model of quark and lepton masses utilizing the binary tetrahedral
($T^{\prime}$) flavor symmetry, or horizontal symmetry, is proposed which
produces the first two generation of quark masses through their interactions
with vector-like quarks that carry charges under an additional $U(1)$. By
softly-breaking the $T^{\prime}$ to a residual $Z_4$ through the vector-like
quark masses, a CKM mixing angle close to the Cabibbo angle is produced. In
order to generate the cobimaximal neutrino oscillation pattern
($\theta_{13}\neq0,\theta_{23}=\pi/4,\delta_{CP}=\pm \pi/2$) and protect the
horizontal symmetry from arbitrary corrections in the lepton sector, there are
automatically two stabilizing symmetries in the dark sector. Several benchmark
cases where the correct relic density is achieved in a multi-component DM
scenario, as well as the potential collider signatures of the vector-like
quarks are discussed.


title: Graphs with large girth and nonnegative curvature dimension condition

abstract:
  In this paper, we classify unweighted graphs satisfying the curvature
dimension condition CD(0,\infty) whose girth are at least five.


title:
Incremental Minimax Optimization based Fuzzy Clustering for Large
  Multi-view Data

abstract:
  Incremental clustering approaches have been proposed for handling large data
when given data set is too large to be stored. The key idea of these approaches
is to find representatives to represent each cluster in each data chunk and
final data analysis is carried out based on those identified representatives
from all the chunks. However, most of the incremental approaches are used for
single view data. As large multi-view data generated from multiple sources
becomes prevalent nowadays, there is a need for incremental clustering
approaches to handle both large and multi-view data. In this paper we propose a
new incremental clustering approach called incremental minimax optimization
based fuzzy clustering (IminimaxFCM) to handle large multi-view data. In
IminimaxFCM, representatives with multiple views are identified to represent
each cluster by integrating multiple complementary views using minimax
optimization. The detailed problem formulation, updating rules derivation, and
the in-depth analysis of the proposed IminimaxFCM are provided. Experimental
studies on several real world multi-view data sets have been conducted. We
observed that IminimaxFCM outperforms related incremental fuzzy clustering in
terms of clustering accuracy, demonstrating the great potential of IminimaxFCM
for large multi-view data analysis.


title:
A simple linear space algorithm for computing a longest common
  increasing subsequence

abstract:
  This paper reformulates the problem of finding a longest common increasing
subsequence of the two given input sequences in a very succinct way. An
extremely simple linear space algorithm based on the new formula can find a
longest common increasing subsequence of sizes $n$ and $m$ respectively, in
time $O(nm)$ using additional $\min\{n,m\}+1$ space.


title:
Simultaneous Realization of Coherent Perfect Absorber and Laser by
  Zero-Index Media with both Gain and Loss

abstract:
  We investigate a unique type of zero-index medium with both gain and loss
(ZIMGL), whose effective permittivity and permeability are purely imaginary and
of opposite signs. We show analytically that, by using a slab of ZIM-GL with
equal magnitude of loss and gain, coherent perfect absorber (CPA) and laser,
i.e. the socalled CPA-laser, can be achieved simultaneously. CPA-laser has been
found previously in parity-time (PT) symmetric systems. However, the underlying
physics in a PT-symmetric system is distinct from that in a ZIM-GL. By
designing a photonic crystal (PC) composed of core-shell rods, with loss and
gain distributed in either the core or the shell, we have realized such a
ZIM-GL. The CPA-laser functionality of such a PC is also confirmed in our
numerical simulations. Our work provides a different approach for simultaneous
realization of CPA and laser besides PTsymmetric systems.


title:
Theory of linear sweep voltammetry with diffuse charge: unsupported
  electrolytes, thin films, and leaky membranes

abstract:
  Linear sweep and cyclic voltammetry techniques are important tools for
electrochemists and have a variety of applications in engineering. Voltammetry
has classically been treated with the Randles-Sevcik equation, which assumes an
electroneutral supported electrolyte. In this paper, we provide a comprehensive
mathematical theory of voltammetry in electrochemical cells with unsupported
electrolytes and for other situations where diffuse charge effects play a role,
and present analytical and simulated solutions of the time-dependent
Poisson-Nernst-Planck (PNP) equations with generalized Frumkin-Butler-Volmer
(FBV) boundary conditions for a 1:1 electrolyte and a simple reaction. Using
these solutions, we construct theoretical and simulated currentvoltage curves
for liquid and solid thin films, membranes with fixed background charge, and
cells with blocking electrodes. The full range of dimensionless parameters is
considered, including the dimensionless Debye screening length (scaled to the
electrode separation), Damkohler number (ratio of characteristic diffusion and
reaction times) and dimensionless sweep rate (scaled to the thermal voltage per
diffusion time). The analysis focuses on the coupling of Faradaic reactions and
diffuse charge dynamics, although capacitive charging of the electrical double
layers (EDL) is also studied, for early time transients at reactive electrodes
and for non-reactive blocking electrodes. Our work highlights cases where
diffuse charge effects are important in the context of voltammetry, and
illustrates which regimes can be approximated using simple analytical
expressions and which require more careful consideration.


title:
Multi-View Fuzzy Clustering with Minimax Optimization for Effective
  Clustering of Data from Multiple Sources

abstract:
  Multi-view data clustering refers to categorizing a data set by making good
use of related information from multiple representations of the data. It
becomes important nowadays because more and more data can be collected in a
variety of ways, in different settings and from different sources, so each data
set can be represented by different sets of features to form different views of
it. Many approaches have been proposed to improve clustering performance by
exploring and integrating heterogeneous information underlying different views.
In this paper, we propose a new multi-view fuzzy clustering approach called
MinimaxFCM by using minimax optimization based on well-known Fuzzy c means. In
MinimaxFCM the consensus clustering results are generated based on minimax
optimization in which the maximum disagreements of different weighted views are
minimized. Moreover, the weight of each view can be learned automatically in
the clustering process. In addition, there is only one parameter to be set
besides the fuzzifier. The detailed problem formulation, updating rules
derivation, and the in-depth analysis of the proposed MinimaxFCM are provided
here. Experimental studies on nine multi-view data sets including real world
image and document data sets have been conducted. We observed that MinimaxFCM
outperforms related multi-view clustering approaches in terms of clustering
accuracy, demonstrating the great potential of MinimaxFCM for multi-view data
analysis.


title:
Local time penalizations with various clocks for one-dimensional
  diffusions

abstract:
  We study some limit theorems for the law of a generalized one-dimensional
diffusion weighted and normalized by a non-negative function of the local time
evaluated at a parametrized family of random times (which we will call a
clock). As the clock tends to infinity, we show that the initial process
converges towards a new penalized process, which generally depends on the
chosen clock. However, unlike with deterministic clocks, no specific
assumptions are needed on the resolvent of the diffusion. We then give a path
interpretation of these penalized processes via some universal $ \sigma
$-finite measures.


title: Resistive Switching in Aqueous Nanopores by Shock Electrodeposition

abstract:
  Solid-state programmable metallization cells have attracted considerable
attention as memristive elements for Redox-based Resistive Random Access Memory
(ReRAM) for low-power and low-voltage applications. In principle, liquid-state
metallization cells could offer the same advantages for aqueous systems, such
as biomedical lab-on-a-chip devices, but robust resistive switching has not yet
been achieved in liquid electrolytes, where electrodeposition is notoriously
unstable to the formation of fractal dendrites. Here, the recently discovered
physics of shock electrodeposition are harnessed to stabilize aqueous copper
growth in polycarbonate nanopores, whose surfaces are modified with charged
polymers. Stable bipolar resistive switching is demonstrated for 500 cycles
with <10s retention times, prior to any optimization of the geometry or
materials.


title:
Hidden multipolar orders of dipole-octupole doublets on a triangular
  lattice

abstract:
  Motivated by the recent development in strong spin-orbit-coupled materials,
we consider the dipole-octupole doublets on the triangular lattice. We propose
the most general interaction between these unusual local moments. Due to the
spin-orbit entanglement and the special form of its wavefunction, the
dipole-octupole doublet has a rather peculiar property under the lattice
symmetry operation. As a result, the interaction is highly anisotropic in the
pseudospin space, but remarkably, is uniform spatially. We analyze the ground
state properties of this generic model and emphasize the hidden multipolar
orders that emerge from the dipolar and octupolar interactions. We clarify the
quantum mutual modulations between the dipolar and octupolar orders. We predict
the experimental consequences of the multipolar orders and propose the
rare-earth triangular materials as candidate systems for these unusual
properties.


title:
Thermodynamic Measurement of Angular Anisotropy at the Hidden Order
  Transition of URu$_2$Si$_2$

abstract:
  The heavy fermion compound URu$_2$Si$_2$ continues to attract great interest
due to the unidentified hidden order it develops below 17.5K. The unique Ising
character of the spin fluctuations and low temperature quasiparticles is well
established. We present detailed measurements of the angular anisotropy of the
nonlinear magnetization that reveal a $\cos^4 \theta$ Ising anisotropy both at
and above the ordering transition. With Landau theory, we show this implies a
strongly Ising character of the itinerant hidden order parameter.


title:
Infinite-time Exponential Growth of the Euler Equation on
  Two-dimensional Torus

abstract:
  For any $A > 2$, we construct solutions to the two-dimensional incompressible
Euler equations on the torus $\mathbb{T}^2$ whose vorticity gradient
$\nabla\omega$ grows exponentially in time: $$\|\nabla\omega(t,
\cdot)\|_{L^\infty} \gtrsim e^{At},\quad \forall\ t \geq 0.$$


title: Vanishing of relative homology and depth of tensor products

abstract:
  For finitely generated modules $M$ and $N$ over a Gorenstein local ring $R$,
one has $depth M + depth N= depth(M\otimes N) +depth R$, i.e., the depth
formula holds, if $M$ and $N$ are Tor-independent and Tate homology
$\hat{Tor}_{i}^{R}(M,N)$ vanishes for all $i\in\mathbb{Z}$. We establish the
same conclusion under weaker hypotheses: if $M$ and $N$ are
$\mathcal{G}$-relative Tor-independent, then the vanishing of
$\hat{Tor}_{i}^{R}(M,N)$ for all $i\le 0$ is enough for the depth formula to
hold. We also analyze the depth of tensor products of modules and obtain a
necessary condition for the depth formula in terms of $\mathcal{G}$-relative
homology.


title: Turbulence in the Ionized Gas of the Orion Nebula

abstract:
  In order to study the nature, origin, and impact of turbulent velocity
fluctuations in the ionized gas of the Orion Nebula, we apply a variety of
statistical techniques to observed velocity cubes. The cubes are derived from
high resolving power ($R \approx 40,000$) longslit spectroscopy of optical
emission lines that span a range of ionizations. From Velocity Channel Analysis
(VCA), we find that the slope of the velocity power spectrum is consistent with
predictions of Kolmogorov theory between scales of 8 and 22 arcsec (0.02 to
0.05 pc). The outer scale, which is the dominant scale of density fluctuations
in the nebula, approximately coincides with the autocorrelation length of the
velocity fluctuations that we determine from the second order velocity
structure function. We propose that this is the principal driving scale of the
turbulence, which originates in the autocorrelation length of dense cores in
the Orion molecular filament. By combining analysis of the non-thermal line
widths with the systematic trends of velocity centroid versus ionization, we
find that the global champagne flow and smaller scale turbulence each
contribute in equal measure to the total velocity dispersion, with respective
root-mean-square widths of 4-5 km/s. The turbulence is subsonic and can account
for only one half of the derived variance in ionized density, with the
remaining variance provided by density gradients in photoevaporation flows from
globules and filaments. Intercomparison with results from simulations implies
that the ionized gas is confined to a thick shell and does not fill the
interior of the nebula.


title:
Heavy fermion behavior in the quasi-one-dimensional Kondo lattice
  CeCo2Ga8

abstract:
  Dimensionality plays an essential role in determining the anomalous non-Fermi
liquid properties in heavy fermion systems. So far most heavy fermion compounds
are quasi-two-dimensional or three-dimensional. Here we report the synthesis
and systematic investigations of the single crystals of the
quasi-one-dimensional Kondo lattice CeCo$_2$Ga$_8$. Resistivity measurements at
ambient pressure reveal the onset of coherence at $T^*\approx 20\,$K and
non-Fermi liquid behavior with linear temperature dependence over a decade in
temperature from 2 K to 0.1 K. The specific heat increases logarithmically with
lowering temperature between 10 K and 2 K and reaches 800 mJ/mol K$^2$ at 1 K,
suggesting that CeCo$_2$Ga$_8$ is a heavy fermion compound in the close
vicinity of a quantum critical point. Resistivity measurements under pressure
further confirm the non-Fermi liquid behavior in a large temperature-pressure
range. The magnetic susceptibility is found to follow the typical behavior for
a one-dimensional (1D) spin chain from 300 K down to $T^*$, and
first-principles calculations predict flat Fermi surfaces for the itinerant
$f$-electron bands. These suggest that CeCo$_2$Ga$_8$ is a rare example of the
quasi-1D Kondo lattice, but its non-Fermi liquid behaviors resemble those of
the quasi-two-dimensional YbRh$_2$Si$_2$ family. The study of the
quasi-one-dimensional CeCo$_2$Ga$_8$ family may therefore help us to understand
the role of dimensionality on heavy fermion physics and quantum criticality.


title:
Sequential multiple testing with generalized error control: an
  asymptotic optimality theory

abstract:
  The sequential multiple testing problem is considered under two generalized
error metrics. Under the first one, the probability of at least $k$ mistakes,
of any kind, is controlled. Under the second, the probabilities of at least
$k_1$ false positives and at least $k_2$ false negatives are simultaneously
controlled. For each formulation, the optimal expected sample size is
characterized, to a first-order asymptotic approximation as the error
probabilities go to 0, and a novel multiple testing procedure is proposed and
shown to be asymptotically efficient under every signal configuration. These
results are established when the data streams for the various hypotheses are
independent and each local log-likelihood ratio statistic satisfies a certain
Strong Law of Large Numbers. In the special case of i.i.d. observations in each
stream, the gains of the proposed sequential procedures over fixed-sample size
schemes are quantified.


title: The Goodness of Covariance Selection Problem from AUC Bounds

abstract:
  We conduct a study of graphical models and discuss the quality of model
selection approximation by formulating the problem as a detection problem and
examining the area under the curve (AUC). We are specifically looking at the
model selection problem for jointly Gaussian random vectors. For Gaussian
random vectors, this problem simplifies to the covariance selection problem
which is widely discussed in literature by Dempster [1]. In this paper, we give
the definition for the correlation approximation matrix (CAM) which contains
all information about the model selection problem and discuss the pth order
Markov chain model and the $p$th order star network model for the a Gaussian
distribution with Toeplitz covariance matrix. For each model, we compute the
model covariance matrix as well as the KL divergence between the Gaussian
distribution and its model. We also show that if the model order, p, is
proportional to the number of nodes, n, then the model selection is
asymptotically good as the number of nodes, n, goes to infinity since the AUC
in this case is bounded away from one. We conduct some simulations which
confirm the theoretical analysis and also show that the selected model quality
increases as the model order, p, increases.


title:
Convergence of Quotients of AF Algebras in Quantum Propinquity by
  Convergence of Ideals

abstract:
  We introduce a topology on the ideal space of inductive limits of C*-algebras
built by a topological inverse limit of the Fell topologies on the C*-algebras
of the given inductive sequence and we produce conditions for when this
topology agrees with the Fell topology of the inductive limit. With this
topology, we impart criteria for when convergence of ideals of an AF algebra
can provide convergence of quotients in the quantum Gromov-Hausdorff
propinquity building off previous joint work with Latremoliere. These findings
bestow a continuous map from a class of ideals of the Boca-Mundici AF algebra
equipped with various topologies including Jacobson and Fell topologies to the
space of quotients equipped with the propinquity topology.


title: Ambient Sound Provides Supervision for Visual Learning

abstract:
  The sound of crashing waves, the roar of fast-moving cars -- sound conveys
important information about the objects in our surroundings. In this work, we
show that ambient sounds can be used as a supervisory signal for learning
visual models. To demonstrate this, we train a convolutional neural network to
predict a statistical summary of the sound associated with a video frame. We
show that, through this process, the network learns a representation that
conveys information about objects and scenes. We evaluate this representation
on several recognition tasks, finding that its performance is comparable to
that of other state-of-the-art unsupervised learning methods. Finally, we show
through visualizations that the network learns units that are selective to
objects that are often associated with characteristic sounds.


title: AdS$_2$ Holographic Dictionary

abstract:
  We construct the holographic dictionary for both running and constant dilaton
solutions of the 2D Einstein-Maxwell-Dilaton theory obtained by a circle
reduction from 3D gravity with negative cosmological constant. This specific
model ensures that the dual theory has a well defined ultraviolet completion in
terms of a 2D CFT, but our results apply qualitatively to a wider class of 2D
dilaton gravity theories. For each type of solutions we perform holographic
renormalization, compute the exact renormalized one-point functions in the
presence of arbitrary sources, and derive the asymptotic symmetries and
conserved charges. In both cases we find that the scalar operator dual to the
dilaton plays a crucial role in the description of the dynamics. Its source
gives rise to a matter conformal anomaly for the running dilaton solutions,
while its expectation value is the only non trivial observable for constant
dilaton solutions. The role of this operator has been largely overlooked in the
literature. We further show that the only non trivial conserved charges for
running dilaton solutions are the mass and the electric charge, while for
constant dilaton solutions only the electric charge is non zero. However, by
uplifting the solutions to three dimensions we show that constant dilaton
solutions can support non trivial extended symmetry algebras, including the one
found by Comp\`ere, Song and Strominger, in agreement with results by Castro
and Song. Finally, we demonstrate that any solution of this specific dilaton
gravity model can be uplifted to a family of asymptotically AdS$_2\times S^2$
or conformally AdS$_2\times S^2$ solutions of the STU model in four dimensions.
The four dimensional solutions obtained by uplifting the running dilaton
solutions coincide with the so called `subtracted geometries', while those
obtained from the uplift of the constant dilaton ones are new.


title:
Comparison among dimensionality reduction techniques based on Random
  Projection for cancer classification

abstract:
  Random Projection (RP) technique has been widely applied in many scenarios
because it can reduce high-dimensional features into low-dimensional space
within short time and meet the need of real-time analysis of massive data.
There is an urgent need of dimensionality reduction with fast increase of big
genomics data. However, the performance of RP is usually lower. We attempt to
improve classification accuracy of RP through combining other reduction
dimension methods such as Principle Component Analysis (PCA), Linear
Discriminant Analysis (LDA), and Feature Selection (FS). We compared
classification accuracy and running time of different combination methods on
three microarray datasets and a simulation dataset. Experimental results show a
remarkable improvement of 14.77% in classification accuracy of FS followed by
RP compared to RP on BC-TCGA dataset. LDA followed by RP also helps RP to yield
a more discriminative subspace with an increase of 13.65% on classification
accuracy on the same dataset. FS followed by RP outperforms other combination
methods in classification accuracy on most of the datasets.


title: Power of Uninitialized Qubits in Shallow Quantum Circuits

abstract:
  We study the computational power of shallow quantum circuits with $O(\log n)$
initialized and $n^{O(1)}$ uninitialized ancillary qubits, where $n$ is the
input length and the initial state of the uninitialized ancillary qubits is
arbitrary. First, we show that such a circuit can compute any symmetric
function on $n$ bits that is classically computable in polynomial time. Then,
we regard such a circuit as an oracle and show that a polynomial-time classical
algorithm with the oracle can estimate the elements of any unitary matrix
corresponding to a constant-depth quantum circuit on $n$ qubits. Since it seems
unlikely that these tasks can be done with only $O(\log n)$ initialized
ancillary qubits, our results give evidences that adding uninitialized
ancillary qubits increases the computational power of shallow quantum circuits
with only $O(\log n)$ initialized ancillary qubits. Lastly, to understand the
limitations of uninitialized ancillary qubits, we focus on
near-logarithmic-depth quantum circuits with them and show the impossibility of
computing the parity function on $n$ bits.


title:
Multiple Exchange Property for M$^\natural$-concave Functions and
  Valuated Matroids

abstract:
  The multiple exchange property for matroid bases is generalized for valuated
matroids and M$^\natural$-concave set functions. The proof is based on the
Fenchel-type duality theorem in discrete convex analysis. The present result
has an implication in economics: The strong no complementarities (SNC)
condition of Gul and Stacchetti is in fact equivalent to the gross substitutes
(GS) condition of Kelso and Crawford.


title: Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

abstract:
  A 3-path vertex cover in a graph is a vertex subset $C$ such that every path
of three vertices contains at least one vertex from $C$. The parameterized
3-path vertex cover problem asks whether a graph has a 3-path vertex cover of
size at most $k$. In this paper, we give a kernel of $5k$ vertices and an
$O^*(1.7485^k)$-time and polynomial-space algorithm for this problem, both new
results improve previous known bounds.


title:
AstroSat/LAXPC reveals the high energy variability of GRS 1915+105 in
  the chi class

abstract:
  We present the first quick look analysis of data from nine {\it AstroSat}'s
LAXPC observations of GRS 1915+105 during March 2016 when the source had the
characteristics of being in Radio-quiet $\chi$ class. We find that a simple
empirical model of a disk blackbody emission, with Comptonization and a broad
Gaussian Iron line can fit the time averaged 3--80 keV spectrum with a
systematic uncertainty of 1.5\% and a background flux uncertainty of 4\%. A
simple deadtime-corrected Poisson noise level spectrum matches well with the
observed high frequency power spectra till 50 kHz and as expected the data show
no significant high frequency ($> 20$ Hz) features. Energy dependent power
spectra reveal a strong low frequency (2 - 8 Hz) Quasi-periodic oscillation
(LFQPO) and its harmonic along with broad band noise. The QPO frequency changes
rapidly with flux (nearly 4 Hz in ~ 5 hours). With increasing QPO frequency, an
excess noise component appears significantly in the high energy regime (> 8
keV). At the QPO frequencies, the time-lag as a function of energy has a
non-monotonic behavior such that the lags decrease with energy till about 15
-20 keV and then increase for higher energies. These first look results
benchmark the performance of LAXPC at high energies and confirms that its data
can be used for more sophisticated analysis such as flux or frequency-resolved
spectro-timing studies.


title: Virtual homological eigenvalue and mapping torus of pseudo-Anosov maps

abstract:
  In this note, we show that, if a pseudo-Anosov map $\phi:S\to S$ admits a
finite cover whose action on the first homology has spectral radius greater
than $1$, then the monodromy of any fibered structure of any finite cover of
the mapping torus $M_{\phi}$ has the same property.


title: Merits and Qualms of Work Fluctuations in Classical Fluctuation Theorems

abstract:
  Work is one of the most basic notion in statistical mechanics, with work
fluctuation theorems being one central topic in nanoscale thermodynamics. With
Hamiltonian chaos commonly thought to provide a foundation for classical
statistical mechanics, here we present general salient results regarding how
(classical) Hamiltonian chaos generically impacts on nonequilibrium work
fluctuations. For isolated chaotic systems prepared with a microcanonical
distribution, work fluctuations are minimized and vanish altogether in
adiabatic work protocols. For isolated chaotic systems prepared at an initial
canonical distribution at inverse temperature $\beta$, work fluctuations
depicted by the variance of $e^{-\beta W}$ are also minimized by adiabatic work
protocols. This general result indicates that if the variance of $e^{-\beta W}$
diverges for an adiabatic work protocol, then it diverges for all nonadiabatic
work protocols sharing the same initial and final Hamiltonians. How such
divergence explicitly impacts on the efficiency of using the Jarzynski's
equality to simulate free energy differences is studied in a Sinai model. Our
general insights shall boost studies in nanoscale thermodynamics and are of
fundamental importance in designing useful work protocols.


title:
Complex dynamics generated by negative and positive feedback delays of a
  prey-predator system with prey refuge: Hopf bifurcation to Chaos

abstract:
  Various field and laboratory experiments show that prey refuge plays a
significant role in the stability of prey-predator dynamics. On the other hand,
theoretical studies show that delayed system exhibits a much more realistic
dynamics than its non-delayed counterpart. In this paper, we study a
multi-delayed prey-predator model with prey refuge. We consider modified
Holling Type II response function that incorporates the effect of prey refuge
and then introduce two discrete delays in the model system. A negative feedback
delay is considered in the logistic prey growth rate to represent density
dependent feedback mechanism and a positive feedback delay is considered to
represent the gestation time of the predator. Our study reveals that the system
exhibits different dynamical behaviors, viz., stable coexistence, periodic
coexistence or chaos depending on the values of the delay parameters and degree
of prey refuge. The interplay between two delays for a fixed value of prey
refuge has also been determined. It is noticed that these delays work in a
complementary fashion. In addition, using the normal form theory and center
manifold argument, we derive the explicit formulae for determining the
direction of the bifurcation, the stability and other properties of the
bifurcating periodic solutions.


title:
Understanding the role of surface plasmon polaritons in two-dimensional
  achiral nanohole arrays for polarization conversion

abstract:
  We have studied the dependence of the rotation angle and ellipticity on the
sample orientation and incident polarization from metallic nanohole arrays. The
arrays have four-fold symmetry and thus do not possess any intrinsic chirality.
We elucidate the role of surface plasmon polaritons (SPPs) in determining the
extrinsic chirality and we verify the results by using finite-difference
time-domain simulation. Our results have indicated the outgoing reflection
arises from the interference between the nonresonant background, which
preserves the input polarization, and the SPP radiation damping, which is
linearly polarized but carries a different polarization defined by the
vectorial field of SPPs. More importantly, the interference manifests various
polarization states ranging from linear to elliptical across the SPP resonance.
We analytically formulate the outgoing waves based on temporal coupled mode
theory (CMT) and the results agree well with the experiment and simulation.
From CMT, we find the polarization conversion depends on the interplay between
the absorption and radiative decay rates of SPPs and the sample orientation.


title:
Random subgraphs of properly edge-coloured complete graphs and long
  rainbow cycles

abstract:
  A subgraph of an edge-coloured complete graph is called rainbow if all its
edges have different colours. In 1980 Hahn conjectured that every properly
edge-coloured complete graph $K_n$ has a rainbow Hamiltonian path. Although
this conjecture turned out to be false, it was widely believed that such a
colouring always contains a rainbow cycle of length almost $n$. In this paper,
improving on several earlier results, we confirm this by proving that every
properly edge-coloured $K_n$ has a rainbow cycle of length $n-O(n^{3/4})$. One
of the main ingredients of our proof, which is of independent interest, shows
that a random subgraph of a properly edge-coloured $K_n$ formed by the edges of
a random set of colours has a similar edge distribution as a truly random graph
with the same edge density. In particular it has very good expansion
properties.


title:
Functional time series forecasting with dynamic updating: An application
  to intraday particulate matter concentration

abstract:
  Environmental data often take the form of a collection of curves observed
sequentially over time. An example of this includes daily pollution measurement
curves describing the concentration of a particulate matter in ambient air.
These curves can be viewed as a time series of functions observed at equally
spaced intervals over a dense grid. The nature of high-dimensional data poses
challenges from a statistical aspect, due to the so-called `curse of
dimensionality', but it also poses opportunities to analyze a rich source of
information to better understand dynamic changes at short time intervals.
Statistical methods are introduced and compared for forecasting one-day-ahead
intraday concentrations of particulate matter; as new data are sequentially
observed, dynamic updating methods are proposed to update point and interval
forecasts to achieve better accuracy. These forecasting methods are validated
through an empirical study of half-hourly concentrations of airborne
particulate matter in Graz, Austria.


title: $L_p$-Bounds for the \v{C}eby\v{s}ev functional

abstract:
  In this paper several new bounds for the \v{C}eby\v{s}ev functional involving
$L_p$-norm are presented.


title:
Spin waves in the AF state of the $t$-$t'$ Hubbard model on the fcc
  lattice: competing interactions, frustration, and instabilities

abstract:
  Spin waves in the type-III ordered antiferromagnetic state of the frustrated
$t$-$t'$ Hubbard model on the fcc lattice are calculated to investigate
finite-$U$-induced competing interaction and frustration effects on magnetic
excitations and instabilities. Particularly strong competing interactions
generated due to interplay of fcc lattice geometry and magnetic order result in
significant spin wave softening. The calculated spin wave dispersion is found
to be in qualitative agreement with the measured spin wave dispersion in the
pyrite mineral $\rm Mn S_2$ obtained from inelastic neutron scattering
experiments. Instabilities to other magnetic orders (type I, type II, spiral,
non-collinear), as signalled by spin wave energies turning negative, are also
discussed.


title:
The Discrete Logarithm Problem over Prime Fields can be transformed to a
  Linear Multivariable Chinese Remainder Theorem

abstract:
  We show that the classical discrete logarithm problem over prime fields can
be reduced to that of solving a system of linear modular equations.