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We present a reinforcement learning (RL) framework in which the learned policy comes with a machine-checkable certificate of provable adversarial robustness. Our approach, called CAROL, learns a model of the environment. In each learning iteration, it uses the current version of this model and an external abstract interpreter to construct a differentiable signal for provable robustness. This signal is used to guide learning, and the abstract interpretation used to construct it directly leads to the robustness certificate returned at convergence. We give a theoretical analysis that bounds the worst-case accumulative reward of CAROL. We also experimentally evaluate CAROL on four MuJoCo environments with continuous state and action spaces. On these tasks, CAROL learns policies that, when contrasted with policies from the state-of-the-art robust RL algorithms, exhibit: (i) markedly enhanced certified performance lower bounds; and (ii) comparable performance under empirical adversarial attacks.

In reinforcement learning for safety-critical settings, it is often desirable for the agent to obey safety constraints at all points in time, including during training. We present a novel neurosymbolic approach called SPICE to solve this safe exploration problem. SPICE uses an online shielding layer based on symbolic weakest preconditions to achieve a more precise safety analysis than existing tools without unduly impacting the training process. We evaluate the approach on a suite of continuous control benchmarks and show that it can achieve comparable performance to existing safe learning techniques while incurring fewer safety violations. Additionally, we present theoretical results showing that SPICE converges to the optimal safe policy under reasonable assumptions.

The exposure of living organisms to environmental and cellular stresses often causes disruptions in protein homeostasis and can result in protein aggregation. The accumulation of protein aggregates in bacterial cells can lead to significant alterations in the cellular phenotypic behavior, including a reduction in growth rates, stress resistance, and virulence. Several experimental procedures exist for the examination of these stressor-mediated phenotypes. This paper describes an optimized assay for the extraction and visualization of aggregated and soluble proteins from different Escherichia coli strains after treatment with a silver-ruthenium-containing antimicrobial. This compound is known to generate reactive oxygen species and causes widespread protein aggregation. The method combines a centrifugation-based separation of protein aggregates and soluble proteins from treated and untreated cells with subsequent separation and visualization by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) and Coomassie staining. This approach is simple, fast, and allows a qualitative comparison of protein aggregate formation in different E. coli strains. The methodology has a wide range of applications, including the possibility to investigate the impact of other proteotoxic antimicrobials on in vivo protein aggregation in a wide range of bacteria. Moreover, the protocol can be used to identify genes that contribute to increased resistance to proteotoxic substances. Gel bands can be used for the subsequent identification of proteins that are particularly prone to aggregation.

We present Revel, a partially neural reinforcement learning (RL) framework for provably safe exploration in continuous state and action spaces. A key challenge for provably safe deep RL is that repeatedly verifying neural networks within a learning loop is computationally infeasible. We address this challenge using two policy classes: a general, neurosymbolic class with approximate gradients and a more restricted class of symbolic policies that allows efficient verification. Our learning algorithm is a mirror descent over policies: in each iteration, it safely lifts a symbolic policy into the neurosymbolic space, performs safe gradient updates to the resulting policy, and projects the updated policy into the safe symbolic subset, all without requiring explicit verification of neural networks. Our empirical results show that Revel enforces safe exploration in many scenarios in which Constrained Policy Optimization does not, and that it can discover policies that outperform those learned through prior approaches to verified exploration.

Being truthful with patients is a critical foundation of the doctor-patient relationship and is fundamental to development of trust. A professional commitment to truth telling may sometimes contradict other principles of bioethics, which may challenge decision-making for the doctor and/or the treatment team. Practitioners may fail to address all ethical or legal aspects of a case and therefore make inappropriate decisions., Dire la vérité aux patients est un fondement essentiel de la relation médecin-patient et est indispensable au développement de la confiance. Un engagement professionnel à dire la vérité peut parfois contredire d’autres principes de bioéthique, ce qui peut remettre en question la prise de décision du médecin ou de l’équipe traitant. Les praticiens peuvent ne pas aborder tous les aspects éthiques ou juridiques d’un cas et donc prendre des décisions inappropriées.

Many example-guided program synthesis techniques use abstractions to prune the search space. While abstraction-based synthesis has proven to be very powerful, a domain expert needs to provide a suitable abstract domain, together with the abstract transformers of each DSL construct. However, coming up with useful abstractions can be non-trivial, as it requires both domain expertise and knowledge about the synthesizer. In this paper, we propose a new technique for learning abstractions that are useful for instantiating a general synthesis framework in a new domain. Given a DSL and a small set of training problems, our method uses tree interpolation to infer reusable predicate templates that speed up synthesis in a given domain. Our method also learns suitable abstract transformers by solving a certain kind of second-order constraint solving problem in a data-driven way. We have implemented the proposed method in a tool called ATLAS and evaluate it in the context of the BLAZE meta-synthesizer. Our evaluation shows that (a) ATLAS can learn useful abstract domains and transformers from few training problems, and (b) the abstractions learned by ATLAS allow BLAZE to achieve significantly better results compared to manually-crafted abstractions.

Background and aimWomen who are homozygous for the p.C282Y mutation in the HFE gene are at much lower risk of iron overload-related disease than p.C282Y homozygous men, presumably because of the iron-depleting effects of menstruation and pregnancy. We used data from a population cohort study to model the impact of menstruation cessation at menopause on serum ferritin (SF) levels in female p.C282Y homozygotes, with p.C282Y/p.H63D simple or compound heterozygotes and those with neither p.C282Y nor p.H63D mutations (HFE wild types) as comparison groups.MethodsA sample of the Melbourne Collaborative Cohort Study was selected for the "HealthIron" study (n=1438) including all HFE p.C282Y homozygotes plus a random sample stratified by HFE-genotype (p.C282Y and p.H63D). The relationship between the natural logarithm of SF and time since menopause was examined using linear mixed models incorporating spline smoothing.ResultsFor p.C282Y homozygotes, SF increased by a factor of 3.6 (95% CI (1.8, 7.0), P&nbsp

Table S1. Protein secretion profile of WT and Cln3 −/− astrocytes under basal conditions. Differences between levels of secreted proteins in supernatants collected after 6 h, 24 h and 72 h from Cln3 −/− and WT astrocyte cultures grown under basal conditions. Data presented as % change (values from Cln3 −/− astrocyte samples compared to corresponding WT astrocyte values) ± SEM from three biological replicates. (−) indicates proteins whose levels were below quantifiable detection levels. Table S2. Protein secretion profile of WT and Cln3 −/− astrocytes after stimulation. Differences between levels of secreted proteins in supernatants collected from Cln3 −/− and WT astrocytes after activation with LPS/IFNγ for 6 h, 24 h and 72 h. Data presented as % change (Cln3 −/− astrocyte sample values compared to corresponding WT astrocyte values) ± SEM from three biological replicates. (−) indicates proteins whose levels were below quantifiable detection levels. (PDF 676 kb)

This retrospective study assesses postoperative complications with simultaneous staphylectomy and unilateral arytenoid lateralization (SP + UAL) in dogs with laryngeal paralysis and concurrent elongation of the soft palate compared to dogs having a UAL alone. Medical records of dogs having a UAL performed from 2010 to 2013 were reviewed. Twenty-three dogs were diagnosed with a concurrent elongated soft palate and had a SP + UAL performed and 89 dogs were diagnosed with an appropriate soft palate and had only a UAL performed. A telephone questionnaire for long-term postoperative outcomes was completed. Survival probability was not statistically different between the 2 groups. Dogs in the SP + UAL group were more likely to be seen for respiratory distress after surgery (P = 0.05). There was no significant difference between the 2 groups in the number of dogs which developed postoperative aspiration pneumonia. The overall complication rate for both groups was high, with postoperative pneumonia being the most common complication.

Alterations in the gut microbiota have been recently linked to oral iron. We conducted two feeding studies including an initial diet-induced iron-depletion period followed by supplementation with nanoparticulate tartrate-modified ferrihydrite (Nano Fe(III): considered bioavailable to host but not bacteria) or soluble ferrous sulfate (FeSO4: considered bioavailable to both host and bacteria). We applied denaturing gradient gel electrophoresis and fluorescence in situ hybridization for study-1 and 454-pyrosequencing of fecal 16S rRNA in study-2. In study-1, the within-community microbial diversity increased with FeSO4 (P = 0.0009) but not with Nano Fe(III) supplementation. This was confirmed in study-2, where we also showed that iron depletion at weaning imprinted significantly lower within- and between-community microbial diversity compared to mice weaned onto the iron-sufficient reference diet (P < 0.0001). Subsequent supplementation with FeSO4 partially restored the within-community diversity (P = 0.006 in relation to the continuously iron-depleted group) but not the between-community diversity, whereas Nano Fe(III) had no effect. We conclude that (1) dietary iron depletion at weaning imprints low diversity in the microbiota that is not, subsequently, easily recovered; (2) in the absence of gastrointestinal disease iron supplementation does not negatively impact the microbiota; and (3) Nano Fe(III) is less available to the gut microbiota.

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We give a new method for solving a problem originally solved about 20 years ago by Sinnott and Kubert, namely that of computing the cohomology of the universal ordinary distribution with respect to the action of the two-element group generated by complex conjugation. We develop the method in sufficient generality so as to be able to calculate analogous cohomology groups in the function field setting which have not previously been calculated. In particular, we are able to confirm a conjecture of L.~S.~Yin conditional on which Yin was able to obtain results on unit indices generalizing those of Sinnott in the classical cyclotomic case and Galovich-Rosen in the Carlitz cyclotomic case. The Farrell-Tate cohomology theory for groups of finite virtual cohomological dimension plays a key role in our proof of Yin's conjecture. The methods developed in the paper have recently been used by P.~Das to illuminate the structure of the Galois group of the algebraic extension of the rational number field generated by the roots of unity and the algebraic $\Gamma$-monomials. This paper has appeared as Contemp. Math. 224 (1999) 1-27.

We show that any matrix-polynomial combination of free noncommutative random variables each having an algebraic law has again an algebraic law. Our result answers a question raised by a recent paper of Shlyakhtenko and Skoufranis. The result belongs to a family of results with origins outside free probability theory, including a result of Aomoto asserting algebraicity of the Green function of random walk of quite general type on a free group., Comment: 41 pages, LaTeX, no figures. In v2, we added references, corrected typos, reorganized some material, and added explanations. Main results remain the same. In this version, v3, we added references and explanation, and simplified the second half of the proof of the main result

It is well-known that the number of planar maps with prescribed vertex degree distribution and suitable labeling can be represented as the leading coefficient of the $\frac{1}{N}$-expansion of a joint cumulant of traces of powers of an $N$-by-$N$ GUE matrix. Here we undertake the calculation of this leading coefficient in a different way. Firstly, we tridiagonalize the GUE matrix in the manner of Trotter and Dumitriu-Edelman and then alter it by conjugation to make the subdiagonal identically equal to $1$. Secondly, we apply the cluster expansion technique (specifically, the Brydges-Kennedy-Abdesselam-Rivasseau formula) from rigorous statistical mechanics. Thirdly, by sorting through the terms of the expansion thus generated we arrive at an alternate interpretation for the leading coefficient related to factorizations of the long cycle $(12\cdots n)\in S_n$. Finally, we reconcile the group-theoretical objects emerging from our calculation with the labeled mobiles of Bouttier-Di Francesco-Guitter., Comment: 42 pages, LaTeX, 17 figures. The present paper completely supercedes arXiv1203.3185 in terms of methods but addresses a different problem

RFamide-related peptide-3 (RFRP-3) neurons have been shown to inhibit gonadotropin-releasing hormone (GnRH) neuronal activity and hence reproduction in birds and eutherian mammals. They have also been proposed to have a direct hypophysiotropic effect on pituitary gonadotropin release. We used a new RFRP-3 antibody to characterize the cell body distribution and fiber projections of RFRP-3 neurons in the adult female brushtail possum brain. RFRP-3-immunoreactive cell bodies were found scattered within the dorsomedial hypothalamus and the dorsomedial half of the ventromedial hypothalamus, while GnRH neurons were observed scattered rostrocaudally along the lateral septum, rostral to the medial septum. There was a significant 2-fold increase in the RFRP-3 cell body number during the nonbreeding season (summer) compared to the breeding season (winter). Immunoreactive RFRP-3 fibers were distributed throughout the thalamus, preoptic area, and hypothalamus. Very few fibers were observed in the median eminence, especially in the external zone. Intraperitoneal injection of the retrograde tracer Fluoro-Gold resulted in the labeling of 40% of hypophysiotropic tuberoinfundibular dopaminergic (tyrosine hydroxylase-positive) neurons; however

Our main result is an explicit operator-theoretic formula for the number of colored planar maps with a fixed set of stars each of which has a fixed set of half-edges with fixed coloration. The formula bounds the number of such colored planar maps well enough to prove convergence near the origin of generating functions arising naturally in the matrix model context. Such convergence is known but the proof of convergence proceeding by way of our main result is relatively simple. Besides Voiculescu's generalization of Wigner's semicircle law, our main technical tool is an integration identity representing the joint cumulant of several functions of a Gaussian random vector. The latter identity in the case of cumulants of order 2 reduces to one well-known as a means to prove the Poincare inequality. We derive the identity by combining the heat equation with the so-called BKAR formula from constructive quantum field theory and rigorous statistical mechanics., Comment: 19 pages, no figures, LaTeX. This new shorter version uses the BKAR formula to derive the main technical result; the previously given proof has been suppressed. New references to the mathematical physics literature have been added. A co-author has been added. But the main result and its proof, apart from some changes in notation, remain the same

The article reports progress concerning the design of a computer-assisted simulation training (CAST) platform for developing decision-making skills in police students. The overarching aim is to outline a theoretical framework for the design of computer-assisted simulation training to facilitate police students’ development of search techniques in complex interactions within the built environment, learning to apply and perform the five “quick peek” techniques for information gathering and subsequent risk evaluation. The article draws on Luckin’s (2010, 2008) ecology of resources model of learner context, informed with perspectives on reflective thinking from Schön (1983, 1987). The article discusses design issues within the ecology of resources model applied on CAST for complex police situations.

Since the terrorist attacks on the United States in September 2001, an awkward nexus of security and economics has been the primary driver of North American governance. This nexus emerged as a pragmatic response to the poisonous politics of economic integration that ensued after 1994 and the advent of the North American Free Trade Agreement (NAFTA). In 2005, the three NAFTA countries launched the Security and Prosperity Partnership (SPP), aimed at reinvigorating the North American agenda to reflect the realities of security and economics. Unfortunately, the U.S. Department of Homeland Security has become the main focal point for policies affecting America’s borders as the department’s mandate has overwhelmed economic considerations and the policy approach has converged around security and law enforcement. Prospects for a new integration project will remain dim for the foreseeable future. However, the paralysis generated by the security-economics nexus has created new governance space in North America that complements the broad evolution of federal politics in all three NAFTA countries, particularly where proposals for reform of the Department of Homeland Security are concerned.

Since the terrorist attacks on the United States in September 2001, an awkward nexus of security and economics has been the primary driver of North American governance. This nexus emerged as a pragmatic response to the poisonous politics of economic integration that ensued after 1994 and the advent of the North American Free Trade Agreement (NAFTA). In 2005, the three NAFTA countries launched the Security and Prosperity Partnership (SPP), aimed at reinvigorating the North American agenda to reflect the realities of security and economics. Unfortunately, the U.S. Department of Homeland Security has become the main focal point for policies affecting America’s borders as the department’s mandate has overwhelmed economic considerations and the policy approach has converged around security and law enforcement. Prospects for a new integration project will remain dim for the foreseeable future. However, the paralysis generated by the security-economics nexus has created new governance space in North America that complements the broad evolution of federal politics in all three NAFTA countries, particularly where proposals for reform of the Department of Homeland Security are concerned.

We provide a period interpretation for multizeta values (in the function field context) in terms of explicit iterated extensions of tensor powers of Carlitz motives (mixed Carlitz-Tate t-motives). We give examples of combinatorially involved relations that these multizeta values satisfy., 12 pages, LaTeX

We consider random hermitian matrices in which distant above-diagonal entries are independent but nearby entries may be correlated. We find the limit of the empirical distribution of eigenvalues by combinatorial methods. We also prove that the limit has algebraic Stieltjes transform by an argument based on dimension theory of noetherian local rings., Comment: 26 pages, LaTeX Revision includes additional results on consequences of algebracity of Stieltjes transform

Our main result is elementary and concerns the relationship between the multiplicative groups of the coordinate and endomorphism rings of the formal additive group over a field of characteristic $p>0$. The proof involves the combinatorics of base $p$ representations of positive integers in a striking way. We apply the main result to construct a canonical quotient of the module of Coleman power series over the Iwasawa algebra when the base local field is of characteristic $p$. This gives information in a situation which apparently has never previously been investigated., LaTeX, 15 pages

A law of large numbers and a central limit theorem are derived for linear statistics of random symmetric matrices whose on-or-above diagonal entries are independent, but neither necessarily identically distributed, nor necessarily all of the same variance. The derivation is based on systematic combinatorial enumeration, study of generating functions, and concentration inequalities of the Poincare type. Special cases treated, with an explicit evaluation of limiting variances, are generalized Wigner and Wishart matrices., Comment: To appear, Prob. Theory Rel. Fields

We propose a conjecture refining the Stark conjecture St(K/k,S) (Tate's formulation) in the function field case. Of course St(K/k,S) in this case is a theorem due to Deligne and independently to Hayes. The novel feature of our conjecture is that it involves two- rather than one-variable algebraic functions over finite fields. Because the conjecture is formulated in the language and framework of Tate's thesis we have powerful standard techniques at our disposal to study it. We build a case for our conjecture by (i) proving a parallel result in the framework of adelic harmonic analysis which we dub the adelic Stirling formula, (ii) proving the conjecture in the genus zero case and (iii) explaining in detail how to deduce St(K/k,S) from our conjecture. In the genus zero case the class of two-variable algebraic functions thus arising includes all the F_q[T]-solitons previously studied and applied by the author, collaborators and others. Ultimately the inspiration for this paper comes from striking examples given some years ago by R. Coleman and D. Thakur., Comment: v1: 64 pages, LaTeX. v2: 55 pages, LaTeX, smaller font; revised following referee's suggestions (locally rewritten, typos corrected, explanatory remarks added, no global reorganization); to appear in Compositio

By the Lefschetz embedding theorem, a principally polarized $g$-dimensional abelian variety is embedded into projective space by the linear system of $4^g$ half-characteristic theta functions. Suppose we {\em edit} this linear system by dropping all the theta functions vanishing at the origin to order greater than parity requires. We prove that for Jacobians the edited $4\Theta$ linear system still defines an embedding into projective space. Moreover, we prove that the projective models of Jacobians arising from the elementary construction of Jacobians recently given by the author are (after passage to linear hulls) copies of the edited $4\Theta$ model. Thus, for all compact Riemann surfaces, we tie together algebraic and analytic Jacobians in a new way.

We prove an estimate for solutions to the linearized Ricci flow system on closed 3-manifolds. This estimate is a generalization of Hamilton's pinching is preserved estimate for the Ricci curvatures of solutions to the Ricci flow on 3-manifolds with positive Ricci curvature. In our estimate we make no assumption on the curvature of the initial metric. We show that the norm of the solution of the Lichnerowicz Laplacian heat equation (coupled to the Ricci flow) is bounded by a constant (depending on time) times the scalar curvature plus a constant. This relies on a Bochner type formula and establishing the nonnegativity of a degree 4 homogeneous polynomial in 6 variables., Comment: 12 pages, no figures

The fermion mass and mixing angle predictions of a recently proposed framework are investigated for large b and $\tau$ Yukawa couplings. A new allowed region of parameters is found for this large $\tan \beta$ case. The two predictions which are substantially altered, $m_t$ and $\tan \beta$, are displayed, including the dependence on the inputs $|V_{cb}|$, $m_c$, $m_b$ and $\alpha_s$. A simple restriction on this framework yields an additional prediction, for $|V_{cb}|$. If the b,t, and $\tau$ Yukawas are equal at the GUT scale then $|\Vcb|$ is predicted and the top quark mass is constrained to lie in the range $\mt = 179. \pm 4.$ GeV., Comment: (beta), 13 pages pages of text plus figures and captions. OHSTPY-HEP-92-018, LBL-332817, UCB-PTH-92/28, Stanford-92-25

In the standard scenario, the electroweak phase transition is a first order phase transition which completes by the nucleation of critical bubbles. Recently, there has been speculation that the standard picture of the electroweak phase transition is incorrect. Instead, it has been proposed that throughout the phase transition appreciable amounts of both broken and unbroken phases of $SU(2)$ coexist in equilibrium. I argue that this can not be the case. General principles insure that the universe will remain in a homogenous state of unbroken $SU(2)$ until the onset of critical bubble production. In addition, an analytic treatment of the one Higgs doublet, electroweak phase transition in the standard model and minimal extensions is reviewed. Results from the thin wall approximation are compared to results obtained using the Lindes' action. Perhaps the most important quantitative result we can get from an analysis of the phase transition is determination of $\vevphi$ when the phase transition completes. For Higgs boson masses above the current experimental limit, the thin wall approximation determines the value of $\vevphi$ at the end of the phase transition to an accuracy of better than three percent., 11

Expression profile of undifferentiated and differentiated (DD28) CTX0E16 cells. Undifferentiated CTX0E16 cells express a range of neurotransmitter receptors, signalling and disease-associated proteins, which are upregulated during differentiation, as determined by RT-PCR; n = 3 independent experiments carried out in triplicate. Table S1 List of antibodies used in study. Table S2 List and description of primers used in RT-PCR and q-PCR experiments. (PDF 181 kb)

Expression profile of undifferentiated and differentiated (DD28) CTX0E16 cells. Undifferentiated CTX0E16 cells express a range of neurotransmitter receptors, signalling and disease-associated proteins, which are upregulated during differentiation, as determined by RT-PCR; n = 3 independent experiments carried out in triplicate. Table S1 List of antibodies used in study. Table S2 List and description of primers used in RT-PCR and q-PCR experiments. (PDF 181 kb)