---
abstract: 'Canonical tensor product subfactors (CTPS’s) describe, among other things, the embedding of chiral observables in two-dimensional conformal quantum field theories. A new class of CTPS’s is constructed some of which are associated with certain modular invariants, thereby establishing the expected existence of the corresponding two-dimensional theories.'
author:
- |
    K.-H. Rehren\
    [Institut für Theoretische Physik, Universität Göttingen]{}\
    [Bunsenstra[ß]{}e 9, D-37073 Göttingen]{}\
    [E-mail: rehren@theorie.physik.uni-goettingen.de]{}
title: Canonical Tensor Product Subfactors
---

Introduction and results
========================

There is a common mathematical note which recurs again and again in the areas of conformal quantum field theory and modular invariants on the one hand, and asymptotic subfactors and quantum doubles on the other hand. In all these areas, there arise inclusions of von Neumann factors of the form $A\otimes B\subset C$ sharing a “canonical” property (see Def. 1.1 below) for which we call them “canonical tensor product subfactors” (CTPS, cf. [@R1]). E.g., in chiral quantum field theories on $S^1$, CTPS’s describe the violation of Haag duality for disjoint intervals (Jones-Wassermann subfactors, cf. [@KLM; @X2]), or the embedding of a coset model into a given ambient model. In two-dimensional conformal quantum field theories they describe the embedding of chiral subtheories [@R1] which is (incompletely) reflected also by modular invariant coupling matrices [@MS]. Ocneanu’s asymptotic subfactors [@O] which are sometimes regarded as generalized quantum doubles [@EK] are also CTPS’s. The main result in this article is the presentation (Thm. 1.4) of a class of new CTPS’s associated with extensions of closed systems of endomorphisms (Def. 1.2, 1.3). Among them there is a subclass of considerable importance for the understanding of modular invariants. Namely, with every modular invariant constructed by a method due to Böckenhauer, Evans and Kawahigashi [@BEK] one can associate one of the new CTPS’s which, if interpreted as a local inclusion of an algebra of chiral observables into an algebra of two-dimensional observables, allows to prove the existence of a complete two-dimensional local conformal quantum field theory associated with the given modular invariant (Cor. 1.6).

The mathematical abstraction of this physical problem as a problem on von Neumann algebras and subfactors is most efficient. It is based on the seminal realization [@H] that positive-energy representations (“superselection charges”) and their fusion are conveniently expressed in terms of endomorphisms, promoting particle statistics to a unitary operator representation (braiding) on the physical Hilbert space, and identifying the statistical dimension as (the square root of) a Jones index.

Extensions or embeddings of quantum field theories can also be coded into single subfactors [@LR]. The characterization of a subfactor, in turn, in terms of a “Q-system” [@L] is particularly useful in this context since these data directly describe the charged field content of the extended theory in terms of superselection charges of the embedded theory [@LR; @RST]. The new subfactors presented in Thm. 1.4 are also defined by specification of their Q-systems (in terms of certain matrix elements for the transition between two extensions), thus making as close contact with the structure of modular invariants as possible.

CTPS’s are very special cases of “symmetric joint inclusions”, i.e., triples of von Neumann algebras $(A,B,C)$ such that $A$ and $B$ are commuting subalgebras of $C$. After a survey of some general properties of symmetric joint inclusions in Sect. 4, we give a characterization of “normality” for CTPS’s in Proposition 4.3. This is a maximality property which, in the case of the embedding of chiral observables into a two-dimensional conformal quantum field theory, corresponds to the maximally extended chiral algebras and diagonal or permutation invariants [@R1].

The canonical property mentioned before is a natural feature of the embedding of chiral quantum field theories into a two-dimensional conformal quantum field theory, reflecting the independence of left and right moving degrees of freedom [@R1]. It is defined as follows.

[Definition]{} A tensor product subfactor of the form $A\otimes B \subset C$ is called a [*canonical tensor product subfactor (CTPS)*]{} if either $A,B,C$ are type II factors and $C$ considered as an $A\otimes B$-$A\otimes B$ bimodule decomposes into irreducibles which are all tensor products of $A$-$A$ bimodules with $B$-$B$ bimodules, or if $A,B,C$ are type III factors and the dual canonical endomorphism $\theta\equiv\bar\iota\cir\iota\in End(A\otimes B)$ decomposes into irreducibles which are all tensor products of endomorphisms of $A$ with endomorphisms of $B$. Let, in the type III case, $$\theta\simeq\bigoplus_{\alpha,\beta}\; Z_{\alpha,\beta}
  \;\alpha \otimes \beta$$ where the sum extends over two sets of mutually inequivalent irreducible endomorphisms of $A$ and of $B$, respectively. Then we call the matrix of multiplicities $Z$ with non-negative integer entries the [*coupling matrix*]{} of the CTPS. The coupling matrix in the type II case is defined analogously in terms of mutually inequivalent irreducible $A$-$A$ and $B$-$B$ bimodules.

Here, as always throughout this paper, $\iota:A\otimes B\to C$ denotes the inclusion homomorphism of the subfactor under consideration, and $\bar\iota:C\to A\otimes B$ a conjugate homomorphism [@LRo].

In order to state our main result, we have to introduce some further notions. We consider type III von Neumann factors $N$, and denote by $End\fin(N)$ the set of unital endomorphisms $\lambda$ of $N$ with finite dimension $d(\lambda)$.

[Definition]{} A [*closed $N$-system*]{} is a set $\Delta \subset End\fin(N)$ of mutually inequivalent irreducible endomorphisms such that (i) $\id_N\in\Delta$, (ii) if $\lambda\in\Delta$ then there is a conjugate endomorphism $\bar\lambda\in\Delta$, and (iii) if $\lambda,\mu\in\Delta$ then $\lambda\mu$ belongs to $\Sigma(\Delta)$, the set of endomorphisms which are equivalent to finite direct sums of elements from $\Delta$.

[Definition]{} Let $N\subset M$ be a subfactor with inclusion homomorphism $\iota:N\to M$. An [*extension of the closed $N$-system $\Delta$*]{} is a pair $(\iota,\alpha)$, where $\iota$ is as above, and $\alpha$ is a map $\Delta\to End\fin(M)$, $\lambda \mapsto\alpha_\lambda$, such that\
(E1) $\quad\iota\cir\lambda = \alpha_\lambda\cir\iota$,\
(E2) $\quad\iota(Hom(\nu,\lambda\mu))\subset
  Hom(\alpha_\nu,\alpha_\lambda\alpha_\mu)$.

After these preliminaries, we can state our main result.

[Theorem]{} Let $N_1\subset M$ and $N_2\subset M$ be two subfactors of $M$, and $(\iota_1,\alpha^1)$ and $(\iota_2,\alpha^2)$ a pair of extensions of a finite closed $N_1$-system $\Delta_1$ and a finite closed $N_2$-system $\Delta_2$, respectively. Then there exists an irreducible CTPS $$A\equiv N_1\otimes N_2\opp \subset B$$ with dual canonical endomorphism $$\theta\equiv\bar\iota\cir\iota \simeq
  \bigoplus_{\lambda_1\in\Delta_1,\lambda_2\in\Delta_2}
  Z_{\lambda_1,\lambda_2}\; \lambda_1\otimes\lambda_2\opp ,$$ whose coupling matrix $Z$ of multiplicities is given by $$Z_{\lambda_1,\lambda_2} = \dim Hom(\A\lambda1,\A\lambda2) .$$

The special case when $\Delta_i$ are braided systems is of particular interest for the problem of modular invariants in conformal quantum field theory:

[Proposition]{} Assume in addition that the closed systems $\Delta_1$ and $\Delta_2$ are braided with unitary braidings $\eps_1$ and $\eps_2$, respectively, turning $\Pi(\Delta_1)$ and $\Pi(\Delta_2)$ into braided monoidal categories. If for all $\lambda_i,\mu_i\in\Delta_i$ and all $\phi\in Hom(\A\lambda1,\A\lambda2)$, $\psi\in Hom(\A\mu1,\A\mu2)$, one has\
(E3) $\quad(\psi\times\phi)\cir \iota_1(\eps_1(\lambda_1,\mu_1)) =
  \iota_2(\eps_2(\lambda_2,\mu_2))\cir (\phi\times\psi$),\
then the canonical isometry $w_1\in Hom(\theta,\theta^2)$ (defined below in the proof of the Theorem) and the braiding operator $\eps(\theta,\theta)$ naturally induced by the braidings $\eps_1$ and $\eps_2\opp$ satisfy $$\eps(\theta,\theta) w_1 = w_1.$$

This result answers an open question in quantum field theory, where possible matrices $Z$ are classified which are supposed to describe the restriction of a given two-dimensional modular invariant conformal quantum field theory to its chiral subtheories, while it is actually not clear whether any given solution $Z$ does come from a two-dimensional quantum field theory. This turns out to be true for a large class of solutions, obtained in [@BEK]:

[Corollary]{} Let $A: I \mapsto A(I)$ be a chiral net of local observables associated with the open intervals $I\subset \RR$, such that each $A(I)$ is a type III factor. Let $\Delta_{\rm DHR}$ be a closed system of mutually inequivalent irreducible DHR-endomorphisms [@H] of $A$ with finite dimension, localized in some interval $I_0$, and put $N:=A(I_0)$. We assume that $A$ is conformally covariant, implying [@GL] that the system of restrictions $\Delta:=\{\lambda=\lambda_{\rm DHR}\vert_N :
  \lambda_{\rm DHR}\in\Delta_{\rm DHR}\}$ is a closed $N$-system. Let $N_1\subset N$ be a subfactor with canonical endomorphism $\theta
  \in \Sigma(\Delta)$, and $N\subset M$ its Jones extension. Put $$Z_{\lambda,\mu}:= \dim Hom(\alpha^+_\lambda,\alpha^-_\mu)$$ where $\alpha^\pm$ are the pair of $\alpha$-inductions [@LR; @BE; @X1] of endomorphisms of $N$ to endomorphisms of $M$, associated with the braidings given by the DHR statistics and its opposite. Then there is a two-dimensional local conformal quantum field theory described by a net $B:O\mapsto B(O)$ of observables associated with the double-cones $O=I\times J$ in $\RR^2$, containing subnets of left and right chiral observables $A_L$ and $A_R$ both isomorphic with $A$, such that the local inclusions of chiral observables $A_L(I)\times A_R(J)\subset B(O)$ are CTPS’s with coupling matrix $ZC$. (Here $C$ is the matrix describing sector conjugation in $\Delta$.) Equivalently, the restriction of the vacuum representation of the two-dimensional quantum field theory $B$ to its chiral subtheories is given by $$\pi^0\vert_{A_L\otimes A_R} = \sum_{\lambda,\mu\in\Delta}\;
  Z_{\lambda,\bar\mu}\;\pi_\lambda\otimes\pi_\mu.$$

The corollary combines and adapts results from [@BEK; @LR]. The point is that if the dual canonical endomorphism $\theta$ associated with $N\subset M$ belongs to $\Sigma(\Delta)$, then $\alpha$-induction [@LR; @BE; @X1] provides a pair of extensions $(\iota,\alpha^+)$ and $(\iota,\alpha^-)$ which satisfies (E1), (E2) as well as (E3) (e.g., [@BE I; Def. 3.3, Lemma 3.5 and 3.25]). The associated coupling matrix $Z_{\lambda,\mu}$ is automatically a modular invariant [@BEK]. By the characterization of extensions of local quantum field theories given in [@LR Prop. 4.9], the local subfactor $A_L(I_0)\otimes A_R(I_0) \subset B(O_0)$ given by the Thm. 1.4 induces an entire net of subfactors, indexed by the double-cones $O$ of two-dimensional Minkowski space. (The charge conjugation $C$ arises due to an anti-isomorphism between $N\opp$ and $N$, cf.  [@LR Prop. 4.10[*ff*]{}].) The statement of Proposition 1.5 is precisely the criterium given in [@LR] for the resulting two-dimensional quantum field theory to be local.

Thus, every modular invariant found by the $\alpha$-induction method given in [@BEK] indeed corresponds to a two-dimensional local conformal quantum field theory extending the given chiral nets of observables.

Extensions of systems of endomorphisms
======================================

We collect some immediate consequences of the definition of an extension, Def. 1.3, using terminology and notations as in [@DR; @LRo].

[Proposition]{} An extension $(\iota,\alpha)$ of a closed $N$-system gives rise to a monoidal functor from the full monoidal C\* subcategory of $End\fin(N)$ with objects $\Pi(\Delta)$ (the set of finite products of elements from $\Delta$) into the monoidal C\* category $End\fin(M)$. In particular, $\lambda\mu\simeq \bigoplus_\nu N_{\lambda\mu}^\nu\,\nu$ implies $\alpha_\lambda\alpha_\mu\simeq \bigoplus_\nu
  N_{\lambda\mu}^\nu\,\alpha_\nu$ (notwithstanding $\alpha_\lambda$ will be reducible in general), and $\alpha_{\bar\lambda}$ is conjugate to $\alpha_\lambda$.

The functor maps objects $\lambda_1\cir\dots\cir\lambda_n$ to $\alpha_{\lambda_1}\cir\dots\cir\alpha_{\lambda_n}$, and intertwiners $T$ to $\iota(T)$ which are again intertwiners by iteration of (E2). It follows from (E2) that $\alpha$ preserves the fusion rules as stated. In particular, $\alpha_{\id_N}$ is an idempotent within $End\fin(M)$, implying that its dimension is $1$, hence it is invertible and must coincide with $\id_M$. Thus the functor preserves the monoidal unit object. It preserves the right monoidal product of intertwiners trivially, and the left monoidal product by (E1). Conjugacy between $\alpha_{\bar\lambda}$ and $\alpha_\lambda$ is a consequence of the following lemma.

[Lemma]{} Let $(\iota,\alpha)$ be an extension of a closed $N$-system $\Delta$. Let $R\in Hom(\id_N,\bar\lambda\lambda)$ and $\bar R\in Hom(\id_N,\lambda\bar\lambda)$ be a pair of standard isometries solving the conjugate equations $$(1_\lambda\times R_\lambda^*)\cir
  (\bar R_\lambda\times 1_\lambda)=d(\lambda)^{-1}1_\lambda
  = (1_{\bar\lambda}\times \bar R_\lambda^*)\cir
  (R_\lambda\times 1_{\bar\lambda}),$$ and thus implementing the unique left- and right-inverses [@LRo] $\Phi_\lambda$ and $\Psi_\lambda$ for $\lambda\in\Delta$. Then $\iota(R_\lambda)$ and $\iota(\bar R_\lambda)$ induce left- and right-inverses $\Phi_{\alpha_\lambda}$ and $\Psi_{\alpha_\lambda}$ for $\alpha_\lambda$. If either $N\subset M$ has finite index, or $\Delta$ is a finite system, then $d(\alpha_\lambda)=d(\lambda)$, and $\Phi_{\alpha_\lambda}$ and $\Psi_{\alpha_\lambda}$ are the unique standard left- and right-inverses.

The first statement is an obvious consequence of (E2). If the index $d(\iota)^2$ is finite, then (E1) implies $d(\alpha_\lambda)=d(\lambda)$. If $\Delta$ is finite, then the minimal dimensions $d(\alpha_\lambda)$ are uniquely determined by the fusion rules of $\{\alpha_\lambda,\lambda\in\Delta\}$, and the latter coincide with those of $\{\lambda\in\Delta\}$. Hence again $d(\alpha_\lambda)=d(\lambda)$. Since $d(\lambda)$ are also the dimensions associated with the pair of isometries $\iota(R_\lambda)$, $\iota(\bar R_\lambda)$, the last claim follows by [@LRo Thm. 3.11].

Thus, general properties of standard left- and right-inverses [@LRo] are applicable. We shall in the sequel repeatedly exploit the trace property $$d(\rho)\Phi_\rho(S^*T)=d(\tau)\Phi_\tau(TS^*)
\qquad {\rm if}\qquad S,T\in Hom(\rho,\tau)$$ for standard left-inverses of $\rho,\tau\in End\fin(M)$, their multiplicativity $\Phi_{\tau\rho}=\Phi_\tau\Phi_\rho$, as well as the equality of standard left- and right-inverses $\Phi_\rho=\Psi_\rho$ on $Hom(\rho,\rho)$.

Construction of the new CTPS’s
==============================

We shall prove Theorem 1.4 by the specification of “Q-systems” (or “canonical triples”) $(\theta,w,w_1)$, which uniquely determine subfactors [@L].

Longo’s characterization states that $\theta\in End\fin(A)$ is the dual canonical endomorphism associated with $A\subset B$ if (and only if) there is a pair of isometries $w\in Hom(\id_A,\theta)$ and $w_1\in Hom(\theta,\theta^2)$ satisfying\
(Q1) $\quad w^*w_1 = \theta(w^*)w_1 = d(\theta)^{-1/2} \eins_A$,

(Q2) $\quad w_1w_1 = \theta(w_1)w_1$, and

(Q3) $\quad w_1w_1^* = \theta(w_1^*)w_1$.\
Namely, then the map $w_1^*\theta(\,\cdot\,)w_1$ is the minimal conditional expectation onto its image $A_1=w_1^*\theta(A)w_1\subset
A$. For $\iota_1:A_1\to A$ the inclusion map and $\bar\iota_1: A\to A_1$ defined by $\theta=\iota_1\bar\iota_1$, the pair of isometries $w\in Hom(\id_A,\iota_1\bar\iota_1)$ and $\iota_1^{-1}(w_1)\in
Hom(\id_{A_1},\bar\iota_1\iota_1)$ achieves the conjugacy between $\iota_1$ and $\bar\iota_1$. By the Jones construction [@J], then, the subfactor $A_1\subset A$ determines its dual subfactor (the Jones extension) $A\subset B$ such that $\theta=\bar\iota\iota$.

[ of Theorem 1.4]{} First notice that the multiplicity of $\id_A$ in $\theta$ is $Z_{\id_{N_1},\id_{N_2}} = \dim Hom(\id_M,\id_M) = 1$, so the asserted subfactor is automatically irreducible.

In order to show that $\theta$ given in the Theorem is the dual canonical endomorphism associated with a subfactor $A\subset B$, we construct the Q-system $(\theta,w,w_1)$ as follows. We first choose a complete system of mutually inequivalent isometries $W_{(\lambda_1,\lambda_2,l)}\equiv W_l\in A\equiv N\otimes N\opp$, where $l$ is considered as a multi-index $(\lambda_1\in\Delta_1,\lambda_2\in\Delta_2,
l=1,\dots Z_{\lambda_1,\lambda_2})$, and put $$\theta=\sum_l W_l\; (\lambda_1\otimes \lambda_2\opp)(\,\cdot\,)\; W_l^*.$$ The choice of these isometries is immaterial and affects the subfactor to be constructed only by inner conjugation.

Since $Hom(\id_A,\theta)$ is one-dimensional, the isometry $w$ is already fixed up to an irrelevant complex phase: $w=W_0$, where $0$ refers to the multi-index $l=0\equiv(\id_{N_1},\id_{N_2},1)$. The second isometry, $w_1$, must be of the form $$w_1=\sum_{l,m,n} (W_l \times W_m) \cir \TT_{lm}^n \cir W_n^*$$ where $\TT_{lm}^n\in Hom(\nu_1\otimes\nu_2\opp,
(\lambda_1\otimes\lambda_2\opp)\cir(\mu_1\otimes\mu_2\opp))$, since these operators span $Hom(\theta,\theta^2)$.

In turn, $\TT_{lm}^n$ must be of the form $$\TT_{lm}^n = \sum_{e_1,e_2} \zeta_{lm,e_1e_2}^n \; T_{e_1} \otimes
(T_{e_2}^*)\opp \qquad (\zeta_{lm,e_1e_2}^n\in\CC)$$ where $T_{e_i}$ constitute orthonormal bases of the intertwiner spaces $Hom(\nu_i,\lambda_i\mu_i)$, since these operators span the spaces $Hom(\nu_1\otimes\nu_2\opp,
(\lambda_1\otimes\lambda_2\opp)\cir(\mu_1\otimes\mu_2\opp))\equiv
Hom(\nu_1,\lambda_1\mu_1)\otimes Hom(\nu_2\opp,\lambda_2\opp\mu_2\opp)$. Note that if $T\in Hom(\alpha,\beta)$ is isometric in $N$, then $(T^*)\opp \in Hom(\beta,\alpha)\opp \equiv Hom(\alpha\opp,\beta\opp)$ is isometric in $N\opp$. The labels $e_i$ are again multi-indices $(\lambda,\mu,\nu,e=1,\dots \dim Hom(\nu,\lambda\mu))$.

It remains therefore to determine the complex coefficients $\zeta_{lm,e_1e_2}^n$, such that $w_1$ is an isometry satisfying Longo’s relations (Q1–3) above. To specify these coefficients, we equip the spaces $Hom(\A\lambda1,\A\lambda2)$ with the non-degenerate scalar products $(\phi,\phi'):=\LI\lambda1(\phi^*\phi')$ (where $\LI\lambda i$ stand for the induced left-inverses for $\A\lambda i$, $i=1,2$, cf. Lemma 2.2). With respect to these scalar products, we choose orthonormal bases $\{\phi_l,l=1,\dots Z_{\lambda_1,\lambda_2}\}$ for all $\lambda_1\in\Delta_1$, $\lambda_2\in\Delta_2$, and put $$\zeta_{lm,e_1e_2}^n = \sqrt\frac{d(\lambda_2)d(\mu_2)}{d(\theta)d(\nu_2)}
\; \LI\nu1
[\iota_1(T_{e_1}^*)(\phi_l^* \times \phi_m^*)\iota_2(T_{e_2})\phi_n].$$ This formula is only apparently asymmetric under exchange $1\leftrightarrow 2$: by the trace property $d(\lambda_2)
\LI\lambda2(\phi\phi^*) = d(\lambda_1)\LI\lambda1
(\phi^*\phi)$, an orthonormal basis $\psi_l$ of $Hom(\A\lambda2,\A\lambda1)$ differs from $\phi_l^*$ by a factor $\sqrt\frac{d(\lambda_1)}{d(\lambda_2)}$, so that in fact $$\overline{\zeta_{lm,e_1e_2}^n} =
\sqrt\frac{d(\lambda_1)d(\mu_1)}{d(\theta)d(\nu_1)}\;
\LI\nu2
[\iota_2(T_{e_2}^*)(\psi_l^* \times \psi_m^*)\iota_1(T_{e_1})\psi_n] .$$

With these coefficients, condition (Q1) is trivially satisfied, since left multiplication of $w_1$ by $w^*$ singles out the term $l=0$ due to $W_0^*W_l=\delta_{l0}$. This leaves only terms with $\lambda_i=\id_{N_i}$, hence $\mu_i=\nu_i$, for which $T_{e_i}$ are trivial and $\sqrt{d(\theta)}\zeta_{0m,e_1e_2}^n= \delta_{mn}$ (up to cancelling complex phases), so $\sqrt{d(\theta)}w^*w_1 = \sum_n W_nW_n^*=\eins_A$. For $\theta(w^*)w_1$ the argument is essentially the same.

We turn to the conditions (Q2) and (Q3). Whenever we compute either of the four products occurring, we obtain a Kronecker delta $W_s^*W_t=\delta_{st}$ for one pair of the labels $l,m,n,\dots$ involved, while the remaining operator parts are of the form $$\begin{aligned}
(W_l \times W_m \times W_k) \left[(T_{e_1} \times 1_{\kappa_1})T_{f_1}
\otimes (((T_{e_2} \times 1_{\kappa_2})T_{f_2})^*)\opp\right] W_n^*, \\[2pt]
(W_l \times W_m \times W_k) \left[(1_{\lambda_1} \times T_{g_1})T_{h_1}
\otimes (((1_{\lambda_2} \times T_{g_2})T_{h_2})^*)\opp\right] W_n^* \;\end{aligned}$$ for the left- and right-hand side of (Q2), $w_1w_1 = \theta(w_1)w_1$, and in turn, $$\begin{aligned}
(W_l \times W_m) \left[T_{e_1}T_{f_1}^* \otimes ((T_{e_2}T_{f_2}^*)^*)\opp\right]
(W_n \times W_k)^* , \qquad\qquad\qquad \\[2pt]
(W_l \times W_m) \left[(1_{\lambda_1}\!\times\!
  T_{g_1}^*)(T_{h_1}\!\times\! 1_{\kappa_1}) \otimes
(((1_{\lambda_2}\!\times\! T_{g_2}^*)(T_{h_2}\!\times\!
1_{\kappa_2}))^*)\opp\right]
(W_n \times W_k)^*  \end{aligned}$$ for the left- and right-hand side of (Q3), $w_1w_1^* = \theta(w_1^*)w_1$. (In these expressions, we do not specify the respective intertwiner spaces to which the various operators $T$ belong, since these are determined by the context.)

The numerical coefficients of these operators are sums over products of two $\zeta$’s or one $\zeta$ and one $\overline{\zeta}$, respectively, with a summation over one common label $s=1,\dots Z_{\sigma_1,\sigma_2}$ due to the above Kronecker $\delta_{st}$. These sums can be carried out.

Namely, the coefficients of the above operators on both sides of (Q2) involve one factor $\zeta^s_{\dots}$ which is a scalar product of the form $\LI\sigma1(X\phi_s)=(X^*,\phi_s)$ in $Hom(\A\sigma1,\A\sigma2)$, so summation with the operator $\phi_s^*$ contributing to the other factor $\zeta$ yields $\sum_s$ $(X^*,\phi_s)\phi_s^* = X$. Then the coefficients of the above operators on both sides of (Q2) are easily cast into the respective form $$\begin{aligned}
\sum_s\zeta^s_{lm,e_1e_2}\zeta^n_{sk,f_1f_2}
=\sqrt\frac{d(\lambda_2)d(\mu_2)d(\kappa_2)}{d(\theta)^2d(\nu_2)}\times
\qquad\qquad\qquad\qquad\qquad\qquad \\
\LI\nu1[\iota_1(T_{f_1}^*(T_{e_1}^*\times 1_{\kappa_1}))
(\phi_l^*\times\phi_m^*\times\phi_k^*)
\iota_2((T_{e_2}\times 1_{\kappa_2})T_{f_2})
\phi_n], \\
\sum_s\zeta^s_{mk,g_1g_2}\zeta^n_{ls,h_1h_2}=
\sqrt\frac{d(\lambda_2)d(\mu_2)d(\kappa_2)}{d(\theta)^2d(\nu_2)}\times
\qquad\qquad\qquad\qquad\qquad\qquad \\
\LI\nu1[\iota_1(T_{h_1}^*(1_{\lambda_1}\times T_{g_1}^*))
(\phi_l^*\times\phi_m^*\times\phi_k^*)
\iota_2((1_{\lambda_2}\times T_{g_2})T_{h_2})
\phi_n].\end{aligned}$$ Now, since the passage from bases of the form $(T_e\times 1_\kappa)T_f$ to bases $(1_\lambda\times T_g)T_h$ of $Hom(\nu,\lambda\mu\kappa)$ for any fixed $\nu,\lambda,\mu,\kappa$ is described by unitary matrices, equality of both sides of (Q2) follows.

The case of (Q3) is in the same vein, but slightly more involved. In the coefficients on the left-hand $\sum_s\zeta^s_{lm,e_1e_2}\overline{\zeta^s_{nk,f_1f_2}}$, we read again the first factor as a scalar product $(X^*,\phi_s)$ within $Hom(\A\sigma1,\A\sigma2)$ and perform the summation $\sum_s
(X^*,\phi_s)\phi_s^* = X$ with the operator $\phi_s^*$ contributing to the second factor. This yields, after application of the trace property for standard left-inverses, the coefficients on the left-hand side of (Q3) $$\begin{aligned}
\sum_s\zeta^s_{lm,e_1e_2}\overline{\zeta^s_{nk,f_1f_2}}=
\sqrt\frac{d(\lambda_2)d(\mu_2)d(\kappa_2)d(\nu_2)}
{d(\theta)^2d(\sigma_2)^2}
\frac{d(\lambda_1)d(\mu_1)}{d(\sigma_1)}\times \quad\qquad\qquad \\
\LI{\mu_1\lambda}1[(\phi_l^*\times\phi_m^*)
\iota_2(T_{e_2}T_{f_2}^*)
(\phi_n\times\phi_k)
\iota_1(T_{f_1}T_{e_1}^*)].\end{aligned}$$

To compute the coefficients $\sum_s\overline{\zeta^m_{sk,g_1g_2}}\zeta^n_{ls,h_1h_2}$ on the right-hand side of (Q3), we first rewrite the second factor as a scalar product $(\phi_s,X)$ within $Hom(\A\sigma1,\A\sigma2)$. This is achieved by applying the trace property: $$\zeta^n_{ls,h_1h_2} = \sqrt\frac{d(\lambda_2)d(\sigma_2)}{d(\theta)d(\nu_2)}
\frac{d(\lambda_1)d(\sigma_1)}{d(\nu_1)}\;
\LI\sigma1[\phi_s^*\LI\lambda1((\phi_l^*\times 1_{\A\sigma2})
\iota_2(T_{h_2})\phi_n\iota_1(T_{h_1}^*))]$$ Now the sum over $s$ with $\phi_s$ contributing to $\overline{\zeta^m_{sk,g_1g_2}}$ can be performed as before, yielding the coefficients on the right-hand side of (Q3) in the form $$\begin{aligned}
\sum_s\overline{\zeta^m_{sk,g_1g_2}}\zeta^n_{ls,h_1h_2}=
\sqrt\frac{d(\lambda_2)d(\kappa_2)d(\sigma_2)^2}{d(\theta)^2d(\nu_2)d(\mu_2)}
\frac{d(\lambda_1)d(\sigma_1)}{d(\nu_1)} \times
\qquad\qquad\qquad\qquad\qquad \\
\LI{\mu_1\lambda}1
[(\phi_l^*\!\times\!\phi_m^*)
\iota_2((1_{\lambda_2}\!\times\! T_{g_2}^*)(T_{h_2}\!\times\! 1_{\kappa_2}))
(\phi_n\!\times\!\phi_k)
\iota_1((T_{h_1}^*\!\times\! 1_{\kappa_1})(1_{\lambda_1}\!\times\! T_{g_1}))].\end{aligned}$$ Noting that the passage from bases $\sqrt\frac{d(\mu)}{d(\sigma)}T_eT_f^*$ to bases $\sqrt\frac{d(\sigma)}{d(\nu)}(1_{\lambda}\times
T_{g}^*)(T_h\times 1_{\kappa})$ of $Hom(\nu\kappa,\lambda\mu)$ is again described by unitary matrices for any fixed $\nu,\kappa,\lambda,\mu$, we obtain equality of both sides of (Q3).

It remains to show that $w_1$ is an isometry, $w_1^*w_1=1$.

Performing the multiplication $w_1^*w_1$ yields two Kronecker delta’s from the factors $W_l \times W_m$, and two more Kronecker delta’s from the factors $T_{e_1}\otimes (T_{e_2}^*)\opp$. Thus $$w_1^*w_1=\sum_{ns}\left(\sum_{lm,e_1e_2}
\overline{\zeta^s_{lm,e_1e_2}}\zeta^n_{lm,e_1e_2}\right) W_sW_n^*,$$ and we have to perform the sums over $l,m,e_1,e_2$ (involving, as sums over multi-indices, the summation over sectors $\lambda_i,\mu_i\in\Delta_i$ for fixed $\nu_i\in\Delta_i$, $i=1,2$).

It turns out convenient to express $\zeta^n_{lm,e_1e_2}$ as a scalar product $(\phi_m,X)$ within $Hom(\A\mu1,\A\mu2)$ as before (with indices relabelled), and to perform the sum over $m$ first. This yields $$\begin{aligned}
\sum_{lm,e_1e_2}
\overline{\zeta^s_{lm,e_1e_2}}\zeta^n_{lm,e_1e_2}
=\sum_{l,e_1e_2}
\frac{d(\lambda_2)d(\mu_2)}{d(\theta)d(\nu_2)}
\frac{d(\lambda_1)d(\mu_1)}{d(\nu_1)}  \times\qquad\qquad\qquad\qquad \\
\LI\nu1[\phi_s^*\iota_2(T_{e_2}^*)
\left(\phi_l\times\LI\lambda1[(\phi_l^*\times 1_{\A\mu1})
\iota_2(T_{e_2})\phi_n\iota_1(T_{e_1}^*)]\right)\iota_1(T_{e_1})]. \end{aligned}$$ In this expression, we can perform the sums over $(e_1,\mu_1)$ and over $(e_2,\mu_2)$ after a unitary passage from the bases of orthonormal isometries $T_e$ of $Hom(\nu,\lambda\mu)$ to the bases $\sqrt\frac{d(\lambda)d(\nu)}{d(\mu)}
(1_\lambda\times T_{e'_1}^*)(\bar R_\lambda\times 1_\nu)$, and obtain after use of the conjugate equations for $R_\lambda,\bar R_\lambda$ $$\sum_{lm,e_1e_2} \overline{\zeta^s_{lm,e_1e_2}}\zeta^n_{lm,e_1e_2} =
\sum_{l,\lambda_1\lambda_2} \frac{d(\lambda_2)^2}{d(\theta)}\;
\LI\nu1[\RI\lambda2(\phi_l\phi_l^*)\times(\phi_s^*\phi_n)].$$ Here $\RI\lambda2$ ist the standard right-inverse implemented by $\iota_2(\bar R_{\lambda_2})$ which coincides with $\LI\lambda2$ on $Hom(\A\lambda2,\A\lambda2)$, and can be evaluated by the trace property: $\RI\lambda2(\phi_l\phi_l^*)= \LI\lambda2(\phi_l\phi_l^*)
=\frac{d(\lambda_1)}{d(\lambda_2)}\LI\lambda1(\phi_l^*\phi_l)=
\frac{d(\lambda_1)}{d(\lambda_2)}$, while the sum over $l$ yields the multiplicity factor $Z_{\lambda_1,\lambda_2}$. Hence $$\sum_{lm,e_1e_2} \overline{\zeta^s_{lm,e_1e_2}}\zeta^n_{lm,e_1e_2}
  = \left(\sum_{\lambda_1,\lambda_2}
  \frac{d(\lambda_1)d(\lambda_2)Z_{\lambda_1,\lambda_2}}{d(\theta)}\right)
  \LI\nu1(\phi_s^*\phi_n)=\delta_{sn},$$ and hence $w_1^*w_1=\sum_n W_nW_n^*=1$. This completes the proof of the Theorem.

[ of Proposition 1.5]{} Left multiplication of $w_1$ with the induced braiding operator $$\eps(\theta,\theta) = \sum_{mlm'l'} (W_{m'}\times W_{l'})
\cir(\eps_1(\lambda_1,\mu_1) \otimes (\eps_2(\lambda_2,\mu_2)^*)\opp)\cir
(W_l\times W_m)^*$$ amounts to a unitary passage from bases $T_e\in Hom(\nu,\lambda\mu)$ to bases $\eps(\lambda,\mu)T_e\in Hom(\nu,\mu\lambda)$. But by (E3), the coefficients $\zeta^n_{lm,e_1e_2}$ are invariant under these changes of bases. Hence $\eps(\theta,\theta)w_1=w_1$.

Joint inclusions and normality
==============================

The main purpose of this section is to introduce and discuss the notions of “normality” and “essential normality”. These properties are of interest since the embedding of chiral subtheories into two-dimensional conformal quantum field theories should always give rise to essentially normal CTPS’s [@R1]. We start by introducing these and related notions in the broader context of “joint inclusions” of von Neumann algebras, i.e., triples $(A,B,C)$ such that $A\vee B\subset C$. We first record some more or less elementary properties of joint inclusions, before we give a simple characterization of normality in the case of CTPS’s in terms of the coupling matrix.

[Definition]{} Let $\Lambda=(A,B,C)$ be a joint inclusion of von Neumann algebras. We denote by $\Lambda^c:=(B^c,A^c,C)$ the joint inclusion of the relative commutants in $C$. We write $\Lambda_1\subset
  \Lambda_2$ if $C_1=C_2$ and $A_1\subset A_2$, $B_1\subset B_2$, and call $\Lambda_2$ [*intermediate*]{} w.r.t. $\Lambda_1$. We call $\Lambda$ [*symmetric*]{} if $\Lambda\subset\Lambda^c$ (i.e., $A$ and $B$ commute with each other). We call $\Lambda$ [*normal*]{} if $\Lambda=\Lambda^c$ (i.e., $A$ and $B$ are each other’s relative commutants). We call $\Lambda$ [*essentially normal*]{} if $\Lambda^c=\Lambda^{cc}$.

One has the following elementary facts.

[Proposition]{} 1. $\Lambda^c=\Lambda^{ccc}$.\
2. If $\Lambda_1\subset\Lambda_2$ then $\Lambda_2^c\subset\Lambda_1^c$.\
3. If $\Lambda$ is symmetric then $\Lambda \subset \Lambda^{cc}
\subset \Lambda^c$.\
4. $\Lambda$ is essentially normal if and only if $\Lambda$ and $\Lambda^c$ are both symmetric.\
5. Every symmetric $\Lambda$ has a normal intermediate joint inclusion.\
6. If $\Lambda$ is normal then one has $Z(A)=(A\vee B)^c=Z(B)
\supset Z(C)$, so $A$ and likewise $B$ are factors if and only if $A\vee B\subset C$ is irreducible, and in this case $C$ necessarily is also a factor.

Assertions 1.–4. are obvious. A normal intermediate joint inclusion is given by, e.g., $(B^c,B^{cc},C)$. Assertion 6 holds since $(A\vee B)^c= A^c \cap B^c$.

While these statements are in quite some parallelism to the theory of self-adjoint extensions of symmetric unbounded operators, assertion 5 is a departure from this parallelism, since self-adjoint extensions do not always exist for symmetric operators. The parallelism seems to become closer if one restricts to the subclass of tensor product subfactors (canonical or not) which are obviously symmetric joint inclusions. But neither $((\eins\otimes B)^c,(A\otimes\eins)^c,C)$ nor the joint inclusion $((\eins\otimes B)^c,(\eins\otimes B)^{cc},C)$ in 4.2(5) will again be a tensor product subfactor in general.

While we have no general criterium for the existence of normal intermediate tensor product subfactors in general, the following proposition gives a simple characterization of normality in the case of CTPS’s, which entails certain constraints on the structure of $A_1\otimes B_1\subset C$ for which a normal CTPS $A\otimes B\subset C$ can possibly be intermediate. These constraints will apply to the embeddings of left and right chiral subtheories into two-dimensional conformal quantum field theories, which by [@R1] give rise to CTPS’s whose relative commutants are again tensor product subfactors, hence symmetric. Thus these local subfactors are essentially normal CTPS’s by Prop. 4.2(4), and the normal intermediate subfactor corresponds to the maximally extended chiral algebras (going along with permutation modular invariants). We do not evaluate these constraints here, but it is clear that the total dual canonical endomorphism must be of the form $(\bar\iota_A\otimes\bar\iota_B)\cir\theta\cir(\iota_A\otimes\iota_B)
\simeq\bigoplus_\alpha\,(\bar\iota_A\alpha\iota_A)\otimes
(\bar\iota_B\sigma(\alpha)\iota_B)$ where $\theta$ corresponding to the normal intermediate inclusion is of the special “permutational” form (N3) as described in the following proposition.

[Proposition]{} Let $A \otimes B \subset C$ be a CTPS of type III with coupling matrix $Z$, i.e., the dual canonical endomorphism is of the form $$\theta\simeq \bigoplus_{\alpha\in\Delta_A,\beta\in\Delta_B}
  Z_{\alpha,\beta}\;\alpha\otimes\beta ,$$ where $\Delta_A\ni\id_A$ and $\Delta_B\ni\id_B$ are two sets of mutually inequivalent irreducible endomorphisms in $End\fin(A)$ and $End\fin(B)$. Then the following conditions are equivalent.

(N1) The joint inclusion $(A\otimes\eins_B,\eins_A\otimes B,C)$ is normal, i.e., $A\otimes \eins_B$ and $\eins_A\otimes B$ are each other’s relative commutants in $C$.

(N2) The coupling matrix couples no non-trivial sector of $A$ to the trivial sector of $B$, and vice versa, i.e., $$Z_{\alpha,\id_B}=\delta_{\alpha,\id_A} \quad \hbox{\rm and} \quad
  Z_{\id_A,\beta}=\delta_{\beta,\id_B} .$$

(N3) The sets $\Delta_A$ and $\Delta_B$ are closed $A$- and $B$-systems, respectively, i.e., they are both closed under conjugation and fusion. There is a bijection $\sigma:\Delta_A \to\Delta_B$ which preserves the fusion rules, i.e., $$\dim Hom(\alpha_1,\alpha_2\alpha_3) = \dim
  Hom(\sigma(\alpha_1),\sigma(\alpha_2)\sigma(\alpha_3)) .$$ The matrix $Z$ is the permutation matrix for this bijection, i.e., $$Z_{\alpha,\beta} = \delta_{\sigma(\alpha),\beta} .$$

The proof is published in [@R1 Lemma 3.4 and Thm. 3.6].

Making contact with the new CTPS’s in Thm. 1.4, we first point out that in general they will [*not*]{} be normal, since among the coupling matrices constructed in [@BEK] there are those which are not of the form (N2,N3).

The most simple case $N_1=N_2=M$ hence $Z=\eins$ is known for a while [@LR], and clearly [*is*]{} normal by Prop. 4.3. Specifically, it describes the “diagonal” extension of the chiral observables by local two-dimensional observables carrying opposite chiral charges. We conclude from Prop. 4.3 that the left and right chiral observables are each other’s relative commutants within this two-dimensional theory, and the same holds whenever the coupling matrix in Cor. 1.6 satisfies condition (N2,N3), i.e., describes a permutation modular invariant (cf. [@R1]).

In the abstract mathematical setting, the subfactors with $Z=\eins$ constructed in [@LR] were recognized [@M] (up to some trivial tensoring with a type III factor) as the type II asymptotic subfactor [@O] associated with $\sigma(M)\subset M$ where $\sigma\equiv\bigoplus_{\lambda\in\Delta}\lambda$. As the asymptotic subfactor $M \vee M^c\subset M_\infty$ associated with a fixed point inclusion $M^G\subset M$ for an outer action of a group $G$, provides the same category of $M_\infty$-$M_\infty$ bimodules as a fixed point inclusion for an outer action of the quantum double $D(G)$ on $M_\infty$, general asymptotic subfactors in turn are considered [@O; @EK] as generalized quantum doubles.

General asymptotic subfactors are CTPS’s, i.e., $M\vee M^c \simeq
M\otimes M^c$ are in a tensor product position within $M_\infty$, and every irreducible $M\vee M^c$-$M\vee M^c$ bimodule associated with the asymptotic subfactor respects the tensor product [@O]. They are normal, i.e., $M$ and $M^c$ are each other’s relative commutant in $M_\infty$. Moreover, the system of $M_\infty$-$M_\infty$ bimodules associated with an asymptotic subfactor has a non-degenerate braiding [@O; @I]. We do not know at present whether the new CTPS’s always share this braiding property, which ought to be tested with methods as in [@I].

Conclusion
==========

We have shown the existence of a class of new subfactors associated with extensions of closed systems of sectors. The proof proceeds by establishing the corresponding Q-systems in terms of certain matrix elements for the transition between two extensions. The new subfactors are canonical tensor product subfactors and include the asymptotic subfactors.

Among the new subfactors, there are the local subfactors of two-dimensional conformal quantum field theory associated with certain modular invariants, thereby establishing the expected existence of these theories. We also gave a characterization of normality of CTPS’s which corresponds to the maximal subtheories of chiral observables in these models.

I am deeply indebted to Y. Kawahigashi, M. Izumi, T. Matsui, and I. Ojima who made possible my visit to Japan during summer 1999 where the present work was completed. I want to thank all of them as well as H. Kosaki, Y. Watatani, and T. Masuda for discussions, and for their hospitality extended to me at the Department of Mathematical Sciences, University of Tokyo, the Graduate School of Mathematics, Kyushu University, and the Research Institute for Mathematical Sciences, Kyoto University. I also thank H. Kurose for giving me the opportunity to present these results at the workshop “Advances in Operator Algebras” [@R2] held at RIMS, Kyoto. Financial support by a Grant-in-Aid for Scientific Research from the Ministry of Education (Japan) is gratefully acknowledged. Finally, I thank J. Böckenhauer for sending me a preliminary manuscript on related issues from a complementary perspective [@BEp].

[99]{} -3pt Böckenhauer, J., Evans, D.E.: [*Modular invariants, graphs and $\alpha$-induction for nets of subfactors*]{}. I, Commun. Math. Phys. [**197**]{}, 361-386 (1998), II, [*ibid.*]{}  [**200**]{}, 57-103 (1999), and III, [*ibid.*]{} [**205**]{}, 183-229 (1999) Böckenhauer, J., Evans, D.E.: [*Modular invariants from subfactors: Type I coupling matrices and intermediate subfactors*]{}. Preprint math.OA/9911239 (1999) Böckenhauer, J., Evans, D.E., Kawahigashi, Y.: [*On $\alpha$-induction, chiral generators and modular invariants for subfactors*]{}. Preprint math.OA/9904109 (1999), to appear in Commun. Math. Phys. Doplicher, S., Roberts, J.E.: [*A new duality theory for compact groups*]{}. Invent. Math. [**98**]{}, 157-218 (1989) Evans, D.E., Kawahigashi, Y.: Quantum Symmetries on Operator Algebras, Oxford University Press, 1998 Guido, D., Longo, R.: [*The conformal spin and statistics theorem*]{}. Commun. Math. Phys. [**181**]{}, 11-36 (1996) Haag, R.: Local Quantum Physics, Springer, 1996 Izumi, M.: [*The structure of sectors associated with the Longo-Rehren inclusions*]{}. I, Kyoto preprint (1999) Jones, V.F.R.: [*Index for subfactors*]{}. Invent. Math., 1-25 (1983) Kawahigashi, Y., Longo, R., Müger, M.: [*Multi-interval subfactors and modularity of representations in conformal field theory*]{}. Preprint math.OA/9903104 (1999) Longo, R.: [*A duality for Hopf algebras and for subfactors*]{}. I, Commun. Math. Phys. [**159**]{}, 133-150 (1994) Longo, R., Rehren, K.-H.: [*Nets of subfactors*]{}. Rev. Math. Phys. [**7**]{}, 567-597 (1995) Longo, R., Roberts, J.E.: [*A theory of dimension*]{}. K-Theory [**11**]{}, 103-159 (1997) Masuda, T.: [*An analogue of Longo’s canonical endomorphism for bimodule theory and its application to asymptotic inclusions*]{}. Int. J. Math. [**8**]{}, 249-265 (1997) Moore, G., Seiberg, N.: [*Naturality in conformal field theory*]{}. Nucl. Phys. [**B313**]{}, 16-40 (1989) Ocneanu, A.: [*Quantum symmetry, differential geometry, and classification of subfactors*]{}. Univ. Tokyo Seminary Notes [**45**]{} (1991) (notes recorded by Y. Kawahigashi) Rehren, K.-H.: [*Chiral observables and modular invariants*]{}. Preprint hep-th/9903262, to appear in Commun. Math. Phys. Rehren, K.-H.: [*New subfactors associated with closed systems of sectors*]{}. Preprint math.OA/9911148 (1999), contribution to the proceedings of the workshop “Advances in Operator Algebras”, RIMS, Kyoto, Sept. 1999 Rehren, K.-H., Stanev, Ya.S., Todorov, I.T.: [ *Characterizing invariants for local extensions of current algebras*]{}. Commun. Math. Phys. [**174**]{}, 605-633 (1996) Xu Feng: [*New braided endomorphisms from conformal inclusions*]{}. Commun. Math. Phys. [**192**]{}, 349-403 (1998) Xu Feng: [*Jones-Wassermann subfactors for disconnected intervals*]{}. Preprint q-alg/9704003 (1997)


Those who did make it to the ground – many of them complaining of hours spent stuck in the car on the hottest day of the year – were at least rewarded with some hard-fought cricket.

By the end of it, Yorkshire must have felt that they had expended the equivalent of a half-marathon’s worth of energy as Surrey scored 330 after winning the toss, the hosts replying with 15-0.

Steven Davies, the former England wicketkeeper, top-scored for Surrey with 117, his first Championship hundred for almost a year.

Kumar Sangakkara, the former Sri Lanka wicketkeeper, hit 73, his highest score against Yorkshire after his five previous innings against them in all cricket had brought 41 runs at 8.2.

Ben Foakes, the current Surrey wicketkeeper, chipped in with 45 and Tom Curran 32.

Yorkshire were not at their absolute best with the ball or in the field, but they stuck at it gamely and restricted Surrey to a score that looked below par on a good batting pitch.

On a day when the temperature touched the mid-20s, there seemed little doubt that a toss would take place and that Surrey would decline the option to bowl.

There was perhaps a smidgen of help for bowlers early on, but it was mostly hard yakka for captain Andrew Gale and his side.

Initially, Yorkshire were all over Surrey as they conceded just three runs in the first seven overs.

David Willey, indifferent with the ball on debut at Notts, was particularly impressive after Yorkshire took to the field with an unchanged line-up.

Jack Brooks, who shared the new-ball, conceded just two runs in his first three overs and he would have had a wicket in the last of those had Gary Ballance not dropped Arun Harinath on nought at fourth slip.

Willey broke through in the ninth over when Rory Burns nibbled at one that bounced and edged to Jonny Bairstow.

Harinath, on nine, was dropped for a second time with the total on 31, Brooks failing to cling on at long-leg after the left-hander helped round a delivery from Willey.

The opener had a third life on 12 when Adam Lyth dropped him at second slip off Liam Plunkett, only for Plunkett to get him next ball when Harinath, turning to leg, skewed to cover. At 38-2, Yorkshire could be pleased with their start, but they ran into the formidable obstacle of Sangakkara. The 38-year-old went into the game as the division’s leading scorer with 397 runs at 66.16, and he immediately looked in velvet touch as he cover-drove his second delivery for four off Willey.

Sangakkara took three fours off a Plunkett over and caressed the ball with languid ease.

Davies got his game going with a cut for four off Brooks and, at lunch, the picture looked better for Surrey at 96-2.

Straight after lunch, Sangakkara back-cut Steve Patterson for four to reach fifty from 78 balls with nine boundaries.

Davies picked up from where he left off by persuading, on the up, a delivery from Willey to the cover rope – a shot so glorious that you imagined Sangakkara must have played it before the scoreboard confirmed otherwise.

Davies has always been an attractive player to watch, and he soon reached his own half-century from 94 balls with eight fours, raising a century stand with Sangakkara from 168 deliveries.

Moments after surviving a close run-out appeal when he tried a single off Brooks to Willey at mid-off, Sangakkara departed unexpectedly. He appeared to be trying to dink a delivery from Plunkett over the slips but picked out Alex Lees at first slip, who nonchalantly held a difficult high chance.

Sangakkara faced 101 balls and hit 13 fours, and his departure left Surrey 160-3 in the 45th over.

That became 161-4 in the next over when Jason Roy was brilliantly caught low down at third slip by Joe Root off Brooks, the batsman clearly feeling that he had played the ball into the ground, a conviction which the Yorkshire crowd did not agree with as they urged him to “gerr’off the field”.

Yorkshire were held up again as Davies and Foakes added 103 in 27 overs, the former reaching his hundred in the penultimate over before tea from 137 balls.

It took the return of Patterson not long before the second new ball to get rid of both men, Davies driving to short cover and Foakes following soon after when cutting to first slip.

Willey trapped James Burke and Gareth Batty with successive deliveries with the second new ball, and Brooks ended the innings by bowling a driving Curran and having Ravi Rampaul caught by Bairstow off a top-edge.


[Work with video display terminals: evaluation of psychosomatic aspects in a group of VDT operators].
The prevalence of psychosomatic symptoms in a group of VDT telephone operators is evaluated and compared with a control group (people not working at VTDs), by using questionnaires. The results show that psychosomatic symptoms are much more frequent in VDT operators in comparison with the control group.


[Endotoxin (LPS) in the pathogenesis of atherosclerosis].
Recent data on the processes underlying atherogenesis indicate the significant role of endotoxin (lipopolysaccharide - LPS) of the intestinal microflora in the development of vascular lesions. This paper summarizes the literature and material results of their research on the participation of LPS gramnegativnyh bacteria in the initiation and progression of atherosclerosis. We prove that the LPS of gram-negative bacteria interact with TLR4, triggers cytokine cascade with the subsequent formation of atheroma.


Categories

Instead of focusing on the week that was in MLS, Andy and Charles look back on the complicated career of Clint Dempsey as the co-leader in USMNT goals announced his retirement this week. Opinions of him have changed since his return to MLS, but there are plenty of reasons to look back fondly.

Andy and Charles begin by looking back to Sporting's 2-0 win over Minnesota United (2:43). How many passes have Shelton and Rubio completed per goal (12:50)? Then they discuss if Croizet might be coming around (15:00). A trio of attackers have received international call-ups (24:00). Finally, we look forward to Seattle (30:33).

Andy and Charles revisit SKC's win over Portland from the weekend by playing a game of Faux or Fo Real (3:45). Is the defense back? Are the midfielders for real? Then look ahead to the match against Minnesota United (16:41). Specifically who should start in the attack.

Andy and Charles break down the Seattle's 5-0 thrashing of LA Galaxy. Sounders are back from the dead (1:00), Galaxy are bad (8:50). The show wraps up with a discussion of Josef Martinez and how he is perfect for the Atlanta system (20:17).

On today's (TT Premium) episode, Andy sits down with Sporting KC forward Diego Rubio to talk about his game-winning goal in Saturday's 1-0 win over Houston Dynamo (2:30), 16-year-old Gianluca Busio's rapid development (7:30), the team's really tough month of July (14:00), wanting to be a starter but starring as a substitute (16:00), and how the trade to acquire Krisztian Nemeth affects him (23:30).

To support Talkin' Touches on Patreon (and get all interviews the day they're released): https://patreon.com/talkintouches

Andy and Charles breakdown Sporting KC's dominant 3-0 win over Portland (3:30). For the first time in a while, SKC were able to break down a bunkering team (10:55). It looks like the Captain has returned to full health (17:00). Is there a center forward controversy? (20:54). Finally, tough lineup choices Vermes will face down the stretch (39:06).

The MLS segment kicks off with the Fightin' Rooneys (1:00). Maybe he was a better signing than we thought? NYCFC move to within one point of the Supporters' Shield lead with a win over Toronto FC (15:25). Finally, Seattle continue their hot streak against FC Dallas (25:26). Another VAR discussion.

Andy and Charles start the show recapping Sporting KC's 2-0 win over LAFC at the weekend (3:10). With 11 matches remaining roles are beginning to become finalized (15:14). Bad news came out about Jimmy Medranda this week, and replacements were discussed (22:39). Also a look ahead to the Portland match (33:43).

It's transfer deadline day and Andy and Charles break down some of the major moves from around MLS. First up, Cristian Ramirez to LAFC (1:00). Portland brought back Jorge Villafaña and Lucas Melano (10:07), Bill Hamid returns to to D.C. United (18:00), and Montreal make a surprising addition (22:18).

To support Talkin' Touches on Patreon: https://www.patreon.com/talkintouches

On this week's episode Andy and Charles recap Sporting KC's wild 1-0 win in Houston (3:40), Sporting has finally signed the striker everyone has been waiting for: Krisztian Nemeth is back in Kansas City (26:00), along with a new defender, Andreu Fontas (51:00).

To support Talkin' Touches on Patreon: https://www.patreon.com/talkintouches


Dietary habits and counseling focused on phosphate intake in hemodialysis patients with hyperphosphatemia.
To evaluate the dietary habits of hemodialysis patients with hyperphosphatemia and the effects of a dietetic intervention focused on limiting dietary phosphate load. Cross-sectional dietary evaluation and prospective intervention study. Hospital hemodialysis units of Pisa and Pistoia, Italy. Subjects Forty-three stable adult hemodialysis patients, 20 of whom had phosphorus serum levels >5.5 mg/dL. Analysis of dietary composition and of the effects of individual dietetic counseling in an attempt to reduce phosphorus intake while preserving the same protein intake. Differences in nutrient intake between normophosphatemic and hyperphosphatemic patients, and changes in dietary phosphorus and phosphorus-protein ratio, serum phosphate, and calcium-phosphate product after dietetic intervention. No major differences in nutrient intake were detected between hyperphosphatemia and normophosphatemia patients, apart from a lower phosphorus-protein ratio (13.1 +/- 1.7 versus 14.1 +/- 2.1 mg/g, P < .05) in the former. After dietetic intervention in the hyperphosphatemia patients, phosphate and calcium intake decreased significantly (by 100 mg on average), whereas dietary protein did not change. A further decrease of the dietary phosphate-protein ratio (12.5 +/- 1.8 mg/g, P < .05) also occurred. Serum phosphate showed a trend to decrease in the intervention group, whereas the serum calcium-phosphate product decreased significantly (from 66.8 +/- 13.1 to 61.0 +/- 13.8 mg2 /dL2 , P < .05). In compliant and motivated patients, individual dietetic counseling may be useful in reducing phosphate load and in limiting the phosphate burden related to an adequate protein intake, with a potentially favorable impact on calcium-phosphate retention. A phosphate-controlled diet has a role in an integrated therapeutic approach to hyperphosphatemia and positive calcium-phosphorus balance in hemodialysis patients.


/**
 * Copyright (c) 2010-2020 Contributors to the openHAB project
 *
 * See the NOTICE file(s) distributed with this work for additional
 * information.
 *
 * This program and the accompanying materials are made available under the
 * terms of the Eclipse Public License 2.0 which is available at
 * http://www.eclipse.org/legal/epl-2.0
 *
 * SPDX-License-Identifier: EPL-2.0
 */
package org.openhab.binding.bluetooth.bluegiga.internal.command.security;

import org.eclipse.jdt.annotation.NonNullByDefault;
import org.openhab.binding.bluetooth.bluegiga.internal.BlueGigaCommand;

/**
 * Class to implement the BlueGiga command encryptStart.
 *

 * This command starts the encryption for a given connection.
 *

 * This class provides methods for processing BlueGiga API commands.
 *

 * Note that this code is autogenerated. Manual changes may be overwritten.
 *
 * @author Chris Jackson - Initial contribution of Java code generator
 */
@NonNullByDefault
public class BlueGigaEncryptStartCommand extends BlueGigaCommand {
    public static int COMMAND_CLASS = 0x05;
    public static int COMMAND_METHOD = 0x00;

    /**
     * Bonding handle of a device. This handle can be obtained for example from events like: Scan
     * Response Status - If handle is 0xFF, all bondings will be deleted
     *

     * BlueGiga API type is uint8 - Java type is {@link int}
     */
    private int handle;

    /**
     * Create bonding if devices are not already bonded. 0: Do not create bonding. 1: Creating
     * bonding
     *

     * BlueGiga API type is boolean - Java type is {@link boolean}
     */
    private boolean bonding;

    /**
     * Bonding handle of a device. This handle can be obtained for example from events like: Scan
     * Response Status - If handle is 0xFF, all bondings will be deleted
     *
     * @param handle the handle to set as {@link int}
     */
    public void setHandle(int handle) {
        this.handle = handle;
    }

    /**
     * Create bonding if devices are not already bonded. 0: Do not create bonding. 1: Creating
     * bonding
     *
     * @param bonding the bonding to set as {@link boolean}
     */
    public void setBonding(boolean bonding) {
        this.bonding = bonding;
    }

    @Override
    public int[] serialize() {
        // Serialize the header
        serializeHeader(COMMAND_CLASS, COMMAND_METHOD);

        // Serialize the fields
        serializeUInt8(handle);
        serializeBoolean(bonding);

        return getPayload();
    }

    @Override
    public String toString() {
        final StringBuilder builder = new StringBuilder();
        builder.append("BlueGigaEncryptStartCommand [handle=");
        builder.append(handle);
        builder.append(", bonding=");
        builder.append(bonding);
        builder.append(']');
        return builder.toString();
    }
}


Estimation of the average residual reflectance of broadband antireflection coatings.
We deal with optimal two-material antireflection (AR) coatings for the visible and adjacent spectral regions. It has been shown before that, for a given set of input parameters (refractive indices of the substrate, ambient medium and high- and low-index coating materials, and for a given spectral width of the AR coating), such designs consist of one or more clusters of layers of approximately constant optical thickness and number of layers. We show that, through the analysis of many different optimal coatings, it is possible to derive two parameters for a simple empirical expression that relates the residual average reflectance in the AR region to the number of clusters. These parameters are given for all possible combinations of relative spectral bandwidth equal to 2, 3, and 4; low-index to ambient-medium index ratio equal to 1.38 and 1.45; and high-to-low index ratio equal to 1.4, 1.5, and 1.7. The agreement between the numerically and the empirically calculated values of residual average reflectance is excellent. From the information presented the optical thin-film designer can quickly calculate the required number of layers and the overall optical thickness of an AR coating having the desired achievable residual average reflectance.


High mobility group proteins 14 and 17 can space nucleosomes in vitro.
Recently we partially purified from Xenopus laevis ovaries a novel, ATP-dependent, spacing activity that can convert a DNA template consisting of irregularly spaced nucleosomes into a chromatin structure made up of regularly spaced nucleosomes with a repeat length of 160-165 base pairs. In a second independent step, the longer spacing of higher eukaryotic chromatin can be generated by the addition of histone H1. The partially purified spacing fraction contains several proteins that display chromatographic properties and mobilities on polyacrylamide gels similar to high mobility group (HMG) proteins. For that reason, different HMG proteins were tested for their ability to generate chromatin structures with regularly spaced nucleosomes. In this report, using two different nucleosome assembly systems, we show that the addition of phosphorylated HMGs 14 and 17 to the histone octamer results in the formation of chromatin with a repeat length of 160-165 base pairs. The results are similar to those obtained from studies of chromatin structure in simple cells, such as fungi and yeast, and in active genes.


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Directed by: Roberto Bianchi Montero

Stars: Farley Granger, Sylva Koscina and Silvano Tranquilli

Language: Italian – Subtitles: English

Country: Italy

Also known as: Rivelazioni di un maniaco sessuale al capo della squadra mobile, Bad Girls, Bir Manyagin Itiraflari, Confessions of a Sex Maniac, Gymna kormia sta dyhtia tou dolofonou, La morte viene dal buio, O anomalos dolofonos, Penetration, Revelations of a Sex Maniac to the Head of the Criminal Investigation Division, Schön, nackt und liebestoll, The Slasher …is the Sex Maniac!

Description: Inspector Capuana investigates serial murders where the victims of unfaithful wives were get killed as they were having sex with their husbands. A naked woman is found murdered and mutilated in a prosperous small province town in Southern Italy. But who is murdering her? After a while, the killer who wears black fedora, gloves, and trench coat starts photographing unfaithful wives as they start having sex with their lovers and also killing them.

1 of 15 - +

Sleaze Server #1

Sleaze Server #2


Abra Cadabra - Nerds (A1 from the 9 Diss) lyrics

[Hook]
Stand tall till I fall
We don't take no bad up round here, we don't take no bad up at all
Man pop off de ting then garn, skrr out the car don't stall
JD chef up a man watch him crawl
A1 chef up a man watch him crawl
You ever see a big man ball?
How many times did the mandem active
Run man out of their ave's
Duck man down in their estate, man best pray they get to their flats
Duck man down in their estate, man best pray they get to their flats
Any violations, help man's throwing up 6 shots with that strap

[Verse]
Pull up on the 9 then wack him
Dem man dere don't want no beef, they're in jail riding voluntary they're not active
Pull up in the 4 door wizz with Jiggawiththedipper, that's savage
How can my man beef me when the same squad made my man panic
Pick up, pick up that shoe little faggot
Talk about magic, you dun know already, man's on making opp boys vanish
My man ain't active, I swear one time Brad caught him on the mains and splashed him
Talk about 9 God, where what world, little pussy just stop with the chatting
I only got one God that I pray to, after I try blast mans back in
Don't make me phone JiggaJ
JiggaJ that's cutters'R'us you get cheffed
Cutters'R'us you get cheffed
4door 2door skrr with the skeng
Like Poppy I ride to the moon and back[Lyrics from: https:/lyrics.az/abra-cadabra/-/nerds-a1-from-the-9-diss.html]To the Sun and back to the grave for my friends
The heat Kash got, that's hot like lava
I make the whole of the pussios pay
Mazza, mazza, mazza, send a man straight to the father
Hollow tips hit him up, leave him holey
Now he see-through like water
Ounto to the world and back
Right now, we the youngest savages in charge, taking no chat
Still screaming free Daz

[Hook]
Stand tall till I fall
We don't take no bad up round here, we don't take no bad up at all
Man pop off de ting then garn, skrr out the car don't stall
JD chef up a man watch him crawl
A1 chef up a man watch him crawl
You ever see a big man ball?
How many times did the mandem active
Run man out of their ave's
Duck man down in their estate, man best pray they get to their flats
Duck man down in their estate, man best pray they get to their flats
Any violations, help man's throwing up 6 shots with that strap
Stand tall till I fall
We don't take no bad up round here, we don't take no bad up at all
Man pop off de ting then garn, skrr out the car don't stall
JD chef up a man watch him crawl
A1 chef up a man watch him crawl
You ever see a big man ball?


ramblings of an entrepreneurial madman

Saturday Afternoon weekly wrap up

I kind of put off my weekly wrap up because it wasn’t the best week in the world. So far I got 18 calls, 2 of which were returns. Of the remaining 16, 11 were either not interested or did not qualify, which leaves me with 5 leads that I’m currently working. You figure if I close 2 of these, that’s puts my conversion at only slightly over 10% so the second half of the order needs to be much better. Wednesday was excellent and every single person I talked to was a good pitch and prospect, but both Thursday and Friday were complete fucking trash and Monday and Tuesday weren’t that great either.

I’m trying not to over think it too much right now. 18 leads aren’t that many to base a full quality assessment on.

That’s all I’m going to say about that, since I can’t do anything to change it over the weekend. Next week, hopefully things will be better.

So I slept in a little later than normal this morning, but fuck it. I definitely needed the rest. Got up and bought my groceries for the week then went to the gym and worked out. Since then I’ve just been relaxing. I picked up a 6 pack of Sierra Nevada Pale Ale, one of my favorite beers, and threw back a couple with lunch.

I was thinking of shooting down to Chase Field tonight to watch a Diamondback’s game because I have nothing else to do. They are playing the Pirates and I doubt many people will be there, so I’m sure I’ll be able to go and grab a nosebleed seat for like 10 bucks. I’m a Red Sox fan, and I can’t tell you how much it sucks that they rarely come to town, so I have to fill my baseball fix somehow. Only issue is that I spent a decent amount on groceries this morning and if I go to the game I’ll drop another $50 bucks on top of that, so I’m probably going to hold off for now. Although I’ve been trying to go out more so I’m not sitting at home dwelling about shit that I cannot change.

Once things pick up a little bit, I’m going to try and go out more often, even if it’s by myself. Social interaction is important.

I love the ballpark though. The grass is perfect, the hot dogs, the beer; just the whole vibe in general is great. I could care less about the Diamondbacks but catching a glimpse of America’s game is always a good time.

I want to visit California again soon. I miss it, and cannot wait until I have a few extra bucks so I can plan a mini vacation out there. Whether it is driving (I love road trips) or flying, I’m going to go out there for at least 1 long weekend before the end of the year.

Not really sure what my plans are for the rest of the day, but I think I’m just going to take it easy this weekend. I can’t believe it’s already fucking April. Shit needs to pick up at work because this year is flying by and I got goals to meet and money to make.


Q:

How to safely change the session cookie DOMAIN or name in production?

We recently realized that our session cookie is being written out to the fully qualified domain name of our site, www.myapp.com, for example:
MYAPPCOOKIE: 79D5DB83..., domain: www.myapp.com

We want to switch this to being a cookie that can be shared cross subdomain, so any server at myapp.com can use the session cookie as well. For example, we'd like our cookie to store like so:
MYAPPCOOKIE: 79D5DB83..., domain: .myapp.com

We tried just changing our session cookie to use that domain like so:
   Cookie sessionCookie = sessionManager.getSessionIdCookie();
   sessionCookie.setDomain(".myapp.com");

and this works fine in most cases.
We're finding some users can't login after deploying this new code in some situations.  The problem arises when a user:

has been logged into our site in their current browser session, but aren't currently logged in.
they try and login again

It appears there are 2 session cookies in their browser:

a stale cookie from their previous session, with the fully qualified domain name
MYAPPCOOKIE: 79D5DB83..., domain: www.myapp.com

the new session cookie for the session they just logged into, with the new domain setting
MYAPPCOOKIE: 79D5DB83..., domain: .myapp.com

What's the best way to manage this old cookie being around? We've tried adding some code to delete the old cookie if a user doesn't have a session, but there are some paths into our app where this doesn't seem to work.
We're open to renaming the cookie if that might work, and are looking for any suggestions others may have. Thanks!

A:

The following approach solves the problem by renaming the session cookie to something new, copying the old value to the new cookie name if required.
It uses some Apache modules (mod_headers and mod_setenvif) to copy the old cookie value to the new cookie name when the new cookie doesn't already exist.
  # We only want to copy the old cookie to the new cookie name
  # when it doesnt already exist in the request. To do so, we
  # set a "per request" flag which is used to determine if we need
  # to do the "cookie copy operation".

  <IfModule mod_setenvif.c>
    SetEnvIf Cookie "NEW_SESSION_ID=" HAS_NEW_SESSION_ID
  </IfModule mod_setenvif.c>

  # If the cookie "NEW_SESSION_ID" doesnt exist in the request, copy
  # the old cookie value to the new cookie name. This allows seamless
  # switching to the new cookie for users with existing sessions, and
  # also ensure that if we have to rollback our code change for some
  # reason, the old cookie will still be ok. Of course if new sessions
  # are created with the new cookie, then they wouldn't be copied over on
  # rollback, but a similar approach could be used if someone
  # wanted to do so

  <IfModule mod_headers.c>
     RequestHeader edit Cookie "OLD_SESSION_ID=([0-9a-zA-Z\-]*)" "NEW_SESSION_ID=$1 DEBUG_MSG_FOR_REPLACING=TRUE; OLD_SESSION_ID=$1" env=!HAS_NEW_SESSION_ID
  </IfModule mod_headers.c>

Note that you can test if the replace is working by looking for the DEBUG_MSG_FOR_REPLACING cookie value, which I've added for debugging purposes when the replace is done.
The following is some sample code for an endpoint that just dumps the value of the cookies header to the response, which you could use when debugging your Apache changes:
@GET
@Path("dump_cookies")
public Object dumpCookies(@Context HttpServletRequest request)
{
  String result = request.getHeader("Cookie");
  String cookies = result.replace("; ", "
");

  String html = "
Raw
" + result;

  html += "
";
  html += "
Cookies
" + cookies;

  return html;
}

Note that we didn't end up using this solution because of business reasons that stopped us from renaming the cookie.  We ended up using this solution instead which allowed us to keep our cookie name the same.


Portobello

Portobello

Portobello

Features & Benefits

The Portobello sofa was inspired from our last trip to New York – Sleek, contemporary and ever so comfy.
Full Backs or Scatter Backs (Box Scatters) available
Dunlop Stamina 30/30, 400g Dacron
Croclock Mechanism
Floating Base


We are seeking an Assistant Office Manager that will enthusiastically lead and
manage the overall operations of our Patient Scheduling Team.
An ideal candidate will have:
1-3 years of management experience in the dental front office or a health care
call center
Exceptional verbal and written communication skills
People-person with helpful, friendly, positive, and professional attitude
High-level of computer skills, accurate typing, and detail-oriented
Ability to reason and problem-solving while serving the Scheduling Coordinators
to assist with patient scheduling needs
Knowledge, Skills, Qualifications, Abilities:
Detail-oriented, accurate and thorough
Negotiation and assertive selling skills create sense of urgency to book
appointments
Ability to use phone and computer systems
Excellent oral and written communication skills
Strong listening/comprehension skills
Ability to stay composed and objective
Exhibit patience and empathy
Flexibility and versatility in problem analysis and resolution
Willingness and ability to learn new technologies, such as telephone systems,
Dentrix for dental appointments and all other proprietary business systems
Warm and professional telephone manner; good memory and patience
Ability to multi-task and follow-up to complete tasks
Ability to be courteous, efficient, effective, and patient in a fast-paced
environment
Maintain strict adherence to confidentiality policies


[sociallocker]

AFRICANGLOBE – Struggling with a chronically stagnant economy and one of the highest crime rates in the world, Jamaica is turning for help to a Black nationalist leader who died more than 70 years ago.

Marcus Garvey, who inspired millions of followers worldwide with messages of Black pride and self-reliance, is being resurrected in a new mandatory civics program in schools across Jamaica.

Students from kindergarten through high school are supposed to learn values such as self-esteem, respect for others and personal responsibility by studying Garvey, whom Martin Luther King Jr. called the “first man on a mass scale and level to give Negroes a sense of dignity and destiny.”

But the program almost totally avoids mention of the positions that made Garvey deeply controversial: his promotion of a “back to Africa” movement, his use of the title “provisional president of Africa” and a campaign for racial separation, born of the conviction that Whites are inherently unjust. He even met with the grand wizard of the Ku Klux Klan, leading some mainstream African-American leaders to question his sanity.

American civil rights pioneer W.E.B. Du Bois once called him “the most dangerous enemy of the Negro race.”

The program is a major rethinking of Garvey’s legacy in his Caribbean homeland. He was the first person named a national hero following independence in 1962, and the government put his likeness on coins. But it had declined repeated calls to use his teachings in schools, where history is not a required subject.

“The teaching of Garveyism in schools is something that politicians of all stripes have shied away from partly because of their own intellectual ignorance and partly because they don’t know what to make of this complex subject,” said Robert Hill, a Garvey expert who is professor emeritus at the University of California, Los Angeles.

But Jamaicans take great pride in the achievements of a native son who created an international movement.

“We want all our children to believe they are important to what becomes of this country. Through Marcus Garvey, we see what it means … to admit to no stumbling block that we cannot overcome,” said Amina Blackwood Meeks, the Ministry of Education’s culture director who led efforts to draft the Garvey-infused civics program.

For many Garvey adherents in Jamaica, where reggae luminary Burning Spear once mournfully sang “no one remembers old Marcus Garvey,” the only question is: What took so long?

Born nearly 50 years after the abolition of slavery in Jamaica, Garvey founded the United Negro Improvement Association in 1914 on the island, and then built it into a mass movement in New York from 1919 to 1927. He established a network of “Liberty Halls” as venues for political debate, theater and scholarship around Black themes, raising awareness of African achievements and calling for economic empowerment to circumvent racism.

From his Harlem base, Garvey urged people find pride in their African history, and assured the descendants of slaves that there were no limitations to what they could accomplish. His Pan-African philosophy urged Blacks to return to the continent of their ancestors and he launched the Black Star Line, a fleet of steamships intended to foster trade among African populations worldwide.

During his meteoric rise, he was bitterly opposed by some fellow Black intellectuals, especially Du Bois, who said Garvey was either “a lunatic or a traitor.” In turn, Garvey called Du Bois a “rabid mulatto who needed a horse whipping,” and he dismissed the National Association for the Advancement of Colored People, or NAACP, as seeking Black assimilation into White society.

His movement spoke on behalf of Africans and delegates at one congress elected him “provisional president of Africa.”

Garvey was eventually framed and convicted of mail fraud charges in connection with his steamship line and was deported to Jamaica in 1927.

But in the early decades of the 20th century, when segregation was deeply implanted in the United States and when European colonialism still stretched around the world, Garvey’s words also inspired civil rights figures in America, political leaders in Africa and the Rastafarian movement in Jamaica.

It’s the uplifting and ambitious aspects of Garvey’s life that educators hope will inspire youngsters in modern-day Jamaica, where times are tough for many.

The official unemployment rate is over 14 percent, but many economists believe it’s higher. Nearly 30 percent of high school students dropped out just before their final year in 2011 and standardized test scores are sinking. Over the past decade, the United Nations says, the island had the world’s third-highest murder rate, with about 60 slayings per 100,000 inhabitants. Young slum dwellers use concoctions that promise to transform dark complexions to a cafe-au-lait color.

Some island academics blame many of the country’s woes on the lingering effects of slavery, which was particularly brutal on Jamaica’s sugar plantations.

“We have to use all tools and strategies at our disposal to tell our children and our people in general that, as Garvey said, the black skin is not a badge of shame, but rather a symbol of national greatness,” said Verene A. Shepherd, director of the Institute for Gender and Development Studies at Jamaica’s University of the West Indies. “If Jamaicans from very young are imbued with this kind of thinking, we will see the benefits in years to come.”

But some academics question whether the program can really overcome the lack of economic opportunities in Jamaica, arguing that self-esteem follows achievement, not the other way around. They also say students will ultimately reject efforts to turn a historical figure into nationalistic propaganda.

Hill said he suspects the program will mostly involve “beating the drum for Garvey” while glossing over his complexities.

“If I just say to students, ‘Garvey is a great man and here’s the reasons he was great,’ that hasn’t taught them anything. In fact, the likelihood is you are likely to alienate the very students you are trying to reach because they will recognize it as just a form of ideological brainwashing,” Hill said. “You have to teach Garvey as part of the development of political thought.”

The teachers’ handbook for the new program includes lesson plans using famous Garvey quotes such as “Up, you mighty race, accomplish what you will” to instill personal identity, discipline, courtesy, national pride and heritage. It says economics lessons could highlight Garvey’s experiences as an entrepreneur, while devotionals will include hymns he wrote. Youngsters will be required to keep a journal.

One of the few references to his “back to Africa” call is a suggestion that students “explore ship building, the shipping industry and travel by sea through a project to reconstruct (small models of) the ships of the Black Star Line.”

So far there has been no public opposition to the program from Blacks or Whites, who are accustomed to seeing Garvey as a part of the country’s history and seem happy to have civics of any sort introduced at schools.

Meeks said nothing about the program will be alienating for students or faculty who are not Black.

Several schools declined to allow a reporter inside classrooms to see the civics course in action because orientation was just getting started.

But Education Minister Ronald Thwaites said he’s confident the program will soon be a success, saying that “after many false starts, the campaign of values and attitudes now begin in earnest, rooted and founded” in Garvey.

By; David McFadden

[/sociallocker]


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Acknowledgements

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(q) be the second derivative of q**6/6 - 121*q**5/20 - q**4/6 + 71*q**3/2 + 5*q**2/2 - 4159*q. Find the third derivative of u(g) wrt g.
120*g - 726
Let f(c) = 5057*c**2 + 974*c + 142. Let a(s) = 5056*s**2 + 975*s + 119. Let k(y) = 6*a(y) - 5*f(y). What is the second derivative of k(j) wrt j?
10102
What is the third derivative of 0*c**4 + 9114*c**5 + 162*c**2 - 8971*c**5 + c**4 wrt c?
8580*c**2 + 24*c
Suppose -4*a = -2 - 6, 5*g = 4*a - 358. Let s = 84 + g. What is the first derivative of 5*x**3 + 10 - 3*x**3 - 3 + s*x**3 wrt x?
48*x**2
Let a(r) be the third derivative of -13*r**6/8 + 878*r**3/3 + 3763*r**2. What is the first derivative of a(w) wrt w?
-585*w**2
Let t(i) be the first derivative of -541*i**3/3 + 1315*i**2/2 + 333. Find the second derivative of t(f) wrt f.
-1082
Suppose -3*d + 1 = -17. What is the third derivative of -47 - 8*t**4 + 49 - 69*t**2 + 50*t**2 - 3*t**d wrt t?
-360*t**3 - 192*t
Let u(o) be the second derivative of 58/3*o**3 + 4*o + 49/3*o**4 - 39 - 1/2*o**2. Find the second derivative of u(r) wrt r.
392
Let d(k) be the first derivative of 3297*k**5/5 - 256*k + 3682. Find the first derivative of d(z) wrt z.
13188*z**3
Suppose -22 = -4*n - 2*d, 2*d = 2*n - 2*d + 14. Let y be n + 237/7 - 3/(-21). What is the first derivative of 26 + 36 - 49 + y*k**2 wrt k?
74*k
Let z(h) be the second derivative of 647*h**5/4 + 317*h**4/3 - 87*h. Find the third derivative of z(p) wrt p.
19410
Let j(w) = 903*w**2 + 12*w + 7. Let l(v) = -897*v**2 - 13*v - 8. Let m(d) = -3*j(d) - 2*l(d). Find the second derivative of m(c) wrt c.
-1830
Find the second derivative of -669*a + 1249 + 0*a**3 - 5*a**3 + 14*a**2 - 661*a + 487 + 1331*a wrt a.
-30*a + 28
Let t(r) be the first derivative of 1838*r**5/5 - r**4/4 - 1407*r - 6305. What is the derivative of t(o) wrt o?
7352*o**3 - 3*o**2
Let q(d) = 14535*d - 11088. Let g(r) = 9696*r - 7391. Let i(y) = 7*g(y) - 5*q(y). What is the derivative of i(s) wrt s?
-4803
Let t(o) be the first derivative of 7*o**6/3 - 4*o**5/5 + 8*o**3/3 - 6*o - 2642. What is the third derivative of t(s) wrt s?
840*s**2 - 96*s
Let w = 35756 - 35756. Let b(n) be the second derivative of w*n**3 - 18*n**2 - 9*n + 4 + 11/12*n**4. Find the first derivative of b(y) wrt y.
22*y
What is the first derivative of -4797 + 23*d**2 + 62*d**2 + 11*d**2 - 122*d**2 + 70*d**4 wrt d?
280*d**3 - 52*d
Let i(l) = -l**3 + 34*l**2 + 3*l - 37. Let r be i(34). Find the second derivative of -71*f - r*f + 113*f**2 + 90*f**2 - 25*f wrt f.
406
Let l = -39 + 62. Suppose -25 = -y - l. Find the third derivative of -17*d**3 - d**2 - 5*d**2 - 10*d**y - 26*d**2 wrt d.
-102
Let x = 64 + -51. Find the second derivative of 51*m**2 - 3*m + 4*m - 13*m - 70 + x*m wrt m.
102
Let c be ((-12)/16)/(6/(-16)). What is the second derivative of -19*z - z**5 - 13*z + 0 + 0*z**5 + 1 - 18*z**c wrt z?
-20*z**3 - 36
Let f(a) = a**2 - 24*a + 112. Let j be f(6). What is the third derivative of 0*p**2 + 5*p**2 + j*p**2 - 27 - 149*p**3 + 29 wrt p?
-894
Let j be 61 - (3/(-2))/((-2)/(-4)). What is the third derivative of 34*h**5 - h**6 - j*h**5 + 37*h**2 + 42*h**5 wrt h?
-120*h**3 + 720*h**2
Let t(u) = u**3 + 6*u**2 + u - 7. Let f be t(-5). Let j = -9 + f. What is the third derivative of 154*l**4 + l**3 - 144*l**j + 6*l**2 - l**3 wrt l?
240*l
Let l(t) = -t**2 + 11*t - 19. Let u be l(8). What is the second derivative of 239*o - 313*o + 5*o**u - 38*o**5 + 2*o**5 wrt o?
-620*o**3
Let o(i) = -i**3 + 7*i**2 + 5*i - 24. Let n be o(7). What is the third derivative of 11 - 2*y + 7*y**3 + n*y**4 + 442*y**2 + 2*y - 434*y**2 wrt y?
264*y + 42
Differentiate -78 + 11 - 17 + 3703*v - 7 + 0 with respect to v.
3703
Let g(j) be the third derivative of 308*j**5/15 + 507*j**4/8 - j**3/3 - 86*j**2 + 6*j. What is the second derivative of g(l) wrt l?
2464
Let v(y) be the second derivative of -1268*y**7/21 - 165*y**4 - 590*y. What is the third derivative of v(j) wrt j?
-152160*j**2
Let t(r) = -2*r**2 + 9*r + 20. Let f be t(6). Find the third derivative of -31*a**3 - 27*a**3 + 58*a**3 - 10*a**4 - 2*a**f + 11 wrt a.
-240*a
Let t(y) be the third derivative of -y**8/336 + y**7/35 + y**5/20 + 199*y**4/24 + 1858*y**2. Find the third derivative of t(l) wrt l.
-60*l**2 + 144*l
Suppose 0 = u + u - 12. Suppose 9 = 10*g - 11*g - 5*j, -2*j = -2*g + 18. What is the third derivative of -16*i**2 - 8*i**2 + 23*i**2 + u*i**g wrt i?
720*i**3
Let f be (((-120)/(-18))/(-10))/((-2)/3). Suppose -f + 15 = 2*b. What is the second derivative of 4*j**2 - b*j**3 - 32*j + 38*j - 4*j**2 wrt j?
-42*j
Let b(v) = v**3 + 7*v**2 + 6*v - 1. Let m be b(-6). Let w be (3/(-9))/((-2)/(-282)*m). Find the second derivative of -4*r + 22 + 25 - w + 9*r**4 wrt r.
108*r**2
Suppose 312 = -4*i + 1156. Find the second derivative of 4 - 305*v - 4 - 140*v**2 + 226*v**2 + i*v**2 wrt v.
594
Let t(p) = -11*p - 115. Let n be t(-12). Find the third derivative of 434*x**6 + n*x - 4*x**2 + 431*x**6 - 899*x**6 wrt x.
-4080*x**3
Find the third derivative of 4235*n**6 - 6 + 97*n**2 + 81*n**2 + 0 + 2 - 1080*n**2 wrt n.
508200*n**3
Let l(q) = 169*q**4 - 15*q**3 - 42*q**2 + 10115. Let s(u) = 170*u**4 - 14*u**3 - 35*u**2 + 10117. Let w(j) = -5*l(j) + 6*s(j). Differentiate w(g) wrt g.
700*g**3 - 27*g**2
What is the derivative of -180 + 38 - 264*u - 575*u - 55 - 17 wrt u?
-839
Let d(q) = -1515*q**2 + 266*q + 1. Let k(p) = -p**2 - p + 1. Let j(r) = -d(r) + 3*k(r). What is the second derivative of j(y) wrt y?
3024
Suppose -6636*k - 399 = -6769*k. Let n(h) be the first derivative of 48 + 0*h**k + 0*h**4 + 0*h**2 - 9*h + 44/5*h**5. Find the first derivative of n(a) wrt a.
176*a**3
Suppose -5*d + 2*l = -342, -2*d + 3*l - 2*l + 137 = 0. Suppose 0 = 4*n + 4*r - d, -56 = -3*n - 0*n - 4*r. Differentiate 30*i - 4 - n - 11 + 19 wrt i.
30
Let a be (1 + -1)*14/(-14). Suppose a = -2*h + 3*h. What is the third derivative of -5*n**2 + h*n**2 - 10*n**6 - 5*n**2 wrt n?
-1200*n**3
Let n be -8 + 7 + (1 - (-2 - 1)). Find the second derivative of 11*b + 46*b**3 - n*b - 218 + 224 wrt b.
276*b
Find the second derivative of -5339 - 1482*a**2 - 1898*a + 5339 wrt a.
-2964
Suppose z + 14 = 5*l - 29, -4*l + 17 = 5*z. Let x be (20 - 1) + (0 + -4 - -2). Differentiate -l - x*r + 41*r - 30*r with respect to r.
-6
What is the second derivative of 2 - 359*r + 110*r**3 - 134*r - 476*r + 128*r - 17*r wrt r?
660*r
Let q(i) be the second derivative of 0*i**3 + 0 + 17/10*i**6 + 0*i**4 + 41/2*i**2 - 94*i + 0*i**5. What is the derivative of q(r) wrt r?
204*r**3
Let z be 110/330*(5 + 1)*25. What is the first derivative of -15 - 15 - 16 - z + 5*i wrt i?
5
Let d = 14/185 + 757/2220. Let n(u) be the second derivative of 0*u**2 + 23*u + 0 - d*u**4 - 4*u**3. What is the second derivative of n(g) wrt g?
-10
What is the second derivative of 19*o**4 - 1284*o - 17*o**4 - 19*o**4 - 14*o**2 + 300*o wrt o?
-204*o**2 - 28
Let f be (-30)/1*(108/(-20) - -5). Let q be -2 - (1252/(-5) - f/20). What is the third derivative of 249*z - q*z + 12*z**5 + 2*z**2 wrt z?
720*z**2
Let w be (-10)/20 - (29241/6)/(-3). Suppose -3*b + 21370 = w. What is the third derivative of 6582*t - b*t + 14*t**4 + 20*t**2 wrt t?
336*t
Let w(t) = -t**2 - 5*t - 4. Let k be w(-2). Find the first derivative of u**4 - 13 - 2*u**4 - 166*u**2 + 77*u**2 + 41*u**k wrt u.
-4*u**3 - 96*u
Suppose 0 = -4*k + 30 - 2. Let j be 1/k + (-1649)/(-119). What is the derivative of -3 - 1 + 26*x**2 - j wrt x?
52*x
Let d be -2*(-10)/4*1. Suppose -4 = s - 4*u + 14, 16 = 3*s + 2*u. What is the third derivative of p**d - 24*p**3 + 11*p**s - 4*p**5 + 24*p**3 wrt p?
-180*p**2
Suppose -4*m = -5*y - 39, 5*m - 15 = 2*m - y. Find the third derivative of 5*v**5 - 5*v**5 - 20*v**3 - 1601*v**6 + 29*v**2 + 1600*v**m wrt v.
-120*v**3 - 120
Let x(w) = w**3 + 6*w**2 - 3*w - 6. Let n be x(-6). Suppose 4*u - n = -0. What is the second derivative of -u*j**5 - 8*j**3 + 8*j**3 - 20*j**5 + 4*j wrt j?
-460*j**3
Let m(x) be the first derivative of 0*x**5 + 11*x**3 + 0*x**2 + 0*x**4 + 0*x**6 - 120 + 0*x + 88/7*x**7. Find the third derivative of m(i) wrt i.
10560*i**3
What is the third derivative of -16*q**4 + 18*q**4 + 304*q**5 + 18*q**4 - 24*q**4 - 14*q**2 - 10 wrt q?
18240*q**2 - 96*q
Let k(n) = 108*n**2 + 40*n - 6. Let g = -73 - -76. Let h(l) = 108*l**2 + 40*l - 9. Let p(z) = g*k(z) - 2*h(z). Find the second


List of Important Bird Areas in Michigan

This is the list of Important Bird Areas in Michigan, the status of which is officially recognized.

 Allegan State Game Area
 Au Sable State Forest
 Cross Village Township, Michigan
 Detroit River International Wildlife Refuge
 Fort Custer Recreation Area
 Fort Custer Training Center
 Harsens Island
 Huron-Manistee National Forests
 Lake Erie Metropark
 Ludington State Park
 Pointe Mouillee State Game Area
 Saginaw Bay
 Seney National Wildlife Refuge
 Sleeping Bear Dunes National Lakeshore
 St. Joseph River (Lake Michigan)
 Tawas Point State Park
 Waterloo Recreation Area
 Whitefish Point Light
 Wilderness State Park
 Yankee Springs Recreation Area

References

Category:Important Bird Areas of Michigan
Important Bird Areas


Congressman Trey Gowdy reminded everyone Wednesday that the Speaker of the House does not need to actually be a sitting congressman.

The Constitution dictates “the House of Representatives shall chuse their Speaker and other Officers,” but it does not stipulate that you have to be a sitting member of Congress to run for the leadership position. Gowdy conveniently pointed that out at the end of his statement on Speaker Paul Ryan’s decision not to seek re-election at the end of his term.

After calling Ryan the “smartest kid in the class” and wishing him his wife and their three children “all the best,” the South Carolina Republican addressed “those within Congress who always seemed to have a better idea or a smarter strategy, now is your chance to run for Speaker.” (RELATED: Paul Ryan Probably Never Knew How Many Of His Colleagues Loved Him Until Now)

“To those outside of Congress who always seemed to have a better idea or a smarter strategy,” he added. “You do not have to be a member of the House to be Speaker of the House and hence, now is your chance to run for Speaker.”

Like Ryan, Gowdy recently announced he will not run again at the conclusion of his term.

When asked for comment on the possibility he becomes the first non-sitting member to become the Speaker of the House in U.S. history, a spokeswoman for his office responded simply “not a chance.”

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Q:

How can I get an error when no results are fetched with DB query?

I'm trying to learn and advance with SQLAlchemy. Today I wanted to learn about exceptions it raises.
I'm working on a Pyramid based project, MySQL server (InnoDB) and SQLAlchemy.
I am trying to except all errors since NoResultFound error would not raise or print in console. So I except exc.SQLAlchemyError.
When I query my table and no results are found, it does not raise or catch or except anything whatsoever and continues operating.
Questions:

How can I and How should I query for .all() or .one(), and deal with
the issue of not having any rows returned?
How can I and how should I deal with others SQL or System related errors? I would like to record them and observe them to fix issues.

My code is:
try:
    query = Session.query(MyTable).filter(Terms.column == my_string).all()
except exc.SQLAlchemyError, e:
    print e
    return False

(Instead of exc.SQLAlchemyError, I first tried NoResultFound, e)

A:

Indeed this code will not raise an exception if no records are found. So instead you should throw your own exception:
import logging
try:
    records = Session.query(MyTable).\
        filter(Terms.column == my_string).all()
    if len(records) == 0:
        raise MyException('No records found')
except MyException, e:
    logging.info('No records found')
except exc.SQLAlchemyError, e:
    logging.exception('Some problem occurred')


Q:

Gain of this schematic

I am interested in the following compressor, which I reverse-engineered from a pcb (there might be some mistakes, but I don't think so)

(open the schematic in a separate window to see the small text). The lightning sign is +9V DC and Vin is only AC, with frequencies 20 Hz < f < 800 Hz. The chip is a TL074CN quad op-amp, and there's a jfet which says K192A.
I guessed this is a compressor because it makes sense in this application to have one (e.g. make the bass more rich), but I am otherwise clueless as to what this part of the circuit actually does.
I suspect it does amplify the signal a bit, could you tell me how much? I am in principle only interested in the linear range of the compressor, as my point is to bypass it, but I need to match the input and the output's magnitude.
Of course, if you want to tell me exactly what the circuit does, please by all means, go ahead :)
EDIT: To clarify: In my previous question (see Short circuit or disconnect to bypass a compressor), I wanted to bypass this compressor. In this question, I am interested in its response, particularly in the linear range.

A:

Connect the JFET gate down to 0V to disable the compression that the JFET brings about. As for gain, I can't tell you because the component references as too small to list and ditto the values. But I can say the the lower right-hand op-amp has the answer to the gain it brings about before the compression threshold starts to have its effect.

One error on the circuit - where I've put "shorting this kills compression" - the short should go to 0V not 4.5V.


A large box, covered in holiday wrapping paper and addressed to Mnuchin, was left outside the home of one of his Bel Air neighbors Saturday evening, ABC 7 News reported.

The package was labeled as being from “the American people,” according to the news station.

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Secret Service agents and Los Angeles police, including bomb-squad officers, soon swarmed the area to investigate the package.

In video of the scene taken by an NBC Los Angeles helicopter, an officer can be seen opening the box, dumping out its contents and spreading a dark, unevenly clumped substance across the ground.

AD

The substance ended up being horse manure, police said. And, according to aerial footage, there was a lot of it.

Afterward, at least three officers could be seen standing around the pile, shining flashlights on the manure and moving it around with their feet, presumably to check whether anything else might be hidden in it.

The LAPD told local media on Saturday that the Secret Service is taking over the investigation. The Secret Service said Sunday that it was “aware of this matter” but referred all questions back to Los Angeles police.

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The Bel Air neighborhood is filled with multimillion-dollar mansions and is home to many celebrities.

One resident, Prince Frederic von Anhalt, told CBS Los Angeles that he was blocked from leaving his neighborhood for about two hours while police cleared the scene.

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“We have $50 million homes and we can’t move. We can’t get out,” von Anhalt, an entrepreneur and husband of the late actress Zsa Zsa Gabor, told the news station Saturday night. “That’s bad. They have to find another way.”

It is unclear whether Mnuchin was home during the incident. Representatives for the Treasury Department did not immediately respond to requests for comment Sunday morning.

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According to the LAPD, its bomb squad handles more than 1,000 calls potentially related to bombs every year. Of those calls, about 22 percent actually involve live devices, live military ordnance or illegal explosives.


2016 Giro d'Italia, Stage 12 to Stage 21

The 2016 Giro d'Italia began on 6 May, and stage 21 occurred on 29 May.

Stage 12
19 May 2016 — Noale to Bibione,

Stage 13
20 May 2016 — Palmanova to Cividale del Friuli,

Stage 14
21 May 2016 — Alpago (Farra) to Corvara (Alta Badia),

Stage 15
22 May 2016 — Castelrotto/Kastelruth to Alpe di Siusi/Seiser Alm ,  Individual time trial

Stage 16
24 May 2016 — Bressanone/Brixen to Andalo,

Stage 17
25 May 2016 — Molveno to Cassano d'Adda,

Stage 18
26 May 2016 — Muggiò to Pinerolo,

Stage 19
27 May 2016 — Pinerolo to Risoul (France),

Stage 20
28 May 2016 — Guillestre (France) to Sant'Anna di Vinadio,

Stage 21
29 May 2016 — Cuneo to Torino,

References

Category:2016 Giro d'Italia
Category:Giro d'Italia stages


BRUSSELS (Reuters) - The European Union’s chief Brexit negotiator said on Thursday he was worried by Britain’s plans for the border arrangement with Ireland after it leaves the EU and urged London to come up with “creative proposals”.

The comments from Michel Barnier highlighted the gulf between the two sides on one of the trickiest issues thrown up by Brexit - how it will affect the currently seamless movement of people and goods between the Republic of Ireland, which is an EU member, and British-ruled Northern Ireland.

Britain said last month that there should be no border posts or immigration checks along the 500 km (300 mile) frontier after Brexit. Some 30,000 people make the crossing each day, and businesses from farming to brewing depend on easy movement of goods between north and south.

While Brussels and Dublin also say they want to keep an open border, they say Britain has failed to explain how it would square this with its stated intention to leave the EU’s customs union.

“What I see in the UK’s paper on Ireland and Northern Ireland worries me,” Barnier told a news conference in Brussels.

“The UK wants the EU to suspend the application of its laws, its customs union and its single market at what will be a new external border for the EU, and the UK wants to use Ireland as a kind of test case for the future EU-UK customs relations. This will not happen,” Barnier said.

The EU is also concerned that Britain could use the border between the two Irelands as a way to circumvent tariffs that could be imposed in a post-Brexit EU-UK trade deal.

Slideshow ( 4 images )

Barnier’s remarks coincided with the publication of a set of principles from the European Commission, the EU’s executive, on how the Irish issue should be dealt with. It explicitly stated that the “onus to propose solutions” on Ireland fell on Britain.

The paper also made it clear that a hard border between Ireland and Northern Ireland should be avoided to protect peace on the island. It said that “any physical border infrastructure” should be ruled out, but that required “flexible and imaginative solutions”.

LACK OF PROGRESS

Nearly three months into Brexit talks, EU and Britain negotiators have made little progress on the Irish border and the other issues - expatriate citizens’ rights and the bill that London should pay its EU partners to settle existing financial commitments - that Brussels wants broadly solved before talks on a future trading relationship can start.

The Irish government called on Britain to make “substantive commitments” and provide “workable solutions”. Prime Minister Leo Varadkar reiterated that for all sides to achieve their aim of avoiding a hard border, Britain needed to stay in the customs union or in a similar arrangement for at least a post-Brexit transition phase.

Britain seized on the EU comments about the need for an open border as evidence that British and EU objectives were “closely aligned”.

“In particular the commitment to avoid any physical infrastructure at the border is a very important step forward,” a government spokesman said, adding that the position papers from both sides “clearly provide a good basis on which to continue to make swift progress.”


Florida voters are going to see a medical marijuana legalization initiative on the ballot for the second election cycle in a row. The 2016 version is different than the 2014 version in a handful of ways. The 2014 initiative lost by just 2 percent. An improved initiative, lessons learned from the 2014 campaign, and a higher voter turnout due to a Presidential election will hopefully overcome that 2 percent. Florida residents want medical marijuana, and not the version previously passed by the Florida Legislature that doesn’t really help anyone. The Editorial Board at the Miami-Herald agrees. Per an excerpt from a recently published article by the media outlet:

But this is about sick people. Passage of the amendment means patients will go to a doctor, who can recommend they receive a medical marijuana card. The card will be issued by the Florida Department of Health, giving a patient the right to buy medical marijuana at dispensaries expected to spring up across the state.

Today, 23 states already permit medical cannabis use, and three more are poised to advance similar laws this year. Florida should join the group, primarily for the sake of an ailing population that wants it available.

Floridians have sent a signal they want medical marijuana. For humanitarian reasons, voters should approve the measure this time around.

I love the compassionate approach the outlet took. A lot of media outlets will tout the business side of a reform effort, if they even support it at all. At the end of the day the United for Care campaign is about compassion, and helping sick people get access to a medicine that is proven to be safe and effective. If you live in Florida, tell everyone that you know to vote for the initiative in November!