Extending finite-memory determinacy to multi-player games

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player multi-outcome games. This generalizes a previous result by Brihaye, De Pril and Schewe. We provide a number of example that separate the various criteria we explore.Our proofs are generally constructive, that is, provide upper bounds for the memory required, as well as algorithms to compute the relevant Nash equilibria

Finite type approximations of Gibbs measures on sofic subshifts

Consider a H\"older continuous potential $\phi$ defined on the full shift A^\nn, where $A$ is a finite alphabet. Let X\subset A^\nn be a specified sofic subshift. It is well-known that there is a unique Gibbs measure $\mu_\phi$ on $X$ associated to $\phi$. Besides, there is a natural nested sequence of subshifts of finite type $(X_m)$ converging to the sofic subshift $X$. To this sequence we can associate a sequence of Gibbs measures $(\mu_{\phi}^m)$. In this paper, we prove that these measures weakly converge at exponential speed to $\mu_\phi$ (in the classical distance metrizing weak topology). We also establish a strong mixing property (ensuring weak Bernoullicity) of $\mu_\phi$. Finally, we prove that the measure-theoretic entropy of $\mu_\phi^m$ converges to the one of $\mu_\phi$ exponentially fast. We indicate how to extend our results to more general subshifts and potentials. We stress that we use basic algebraic tools (contractive properties of iterated matrices) and symbolic dynamics.Comment: 18 pages, no figure

Extending Finite Memory Determinacy to Multiplayer Games

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding class of multi-player multi-outcome games. This generalizes a previous result by Brihaye, De Pril and Schewe. For most of our conditions we provide counterexamples showing that they cannot be dispensed with. Our proofs are generally constructive, that is, provide upper bounds for the memory required, as well as algorithms to compute the relevant winning strategies.Comment: In Proceedings SR 2016, arXiv:1607.0269

Interactions, Distribution of Pinning Energies, and Transport in the Bose Glass Phase of Vortices in Superconductors

We study the ground state and low energy excitations of vortices pinned to columnar defects in superconductors, taking into account the long--range interaction between the fluxons. We consider the ``underfilled'' situation in the Bose glass phase, where each flux line is attached to one of the defects, while some pins remain unoccupied. By exploiting an analogy with disordered semiconductors, we calculate the spatial configurations in the ground state, as well as the distribution of pinning energies, using a zero--temperature Monte Carlo algorithm minimizing the total energy with respect to all possible one--vortex transfers. Intervortex repulsion leads to strong correlations whenever the London penetration depth exceeds the fluxon spacing. A pronounced peak appears in the static structure factor $S(q)$ for low filling fractions $f \leq 0.3$. Interactions lead to a broad Coulomb gap in the distribution of pinning energies $g(\epsilon)$ near the chemical potential $\mu$, separating the occupied and empty pins. The vanishing of $g(\epsilon)$ at $\mu$ leads to a considerable reduction of variable--range hopping vortex transport by correlated flux line pinning.Comment: 16 pages (twocolumn), revtex, 16 figures not appended, please contact [email protected]

New insights into orthostatic hypotension in multiple system atrophy: a European multicentre cohort study

Objectives: Orthostatic hypotension (OH) is a key feature of multiple system atrophy (MSA), a fatal progressive neurodegenerative disorder associated with autonomic failure, parkinsonism and ataxia. This study aims (1) to determine the clinical spectrum of OH in a large European cohort of patients with MSA and (2) to investigate whether a prolonged postural challenge increases the sensitivity to detect OH in MSA. Methods: Assessment of OH during a 10 min orthostatic test in 349 patients with MSA from seven centres of the European MSA-Study Group (age: 63.6±8.8 years; disease duration: 4.2±2.6 years). Assessment of a possible relationship between OH and MSA subtype (P with predominant parkinsonism or C with predominant cerebellar ataxia), Unified MSA Rating Scale (UMSARS) scores and drug intake. Results: 187 patients (54%) had moderate (>20 mm Hg (systolic blood pressure (SBP)) and/or >10 mm Hg (diastolic blood pressure (DBP)) or severe OH (>30 mm Hg (SBP) and/or >15 mm Hg (DBP)) within 3 min and 250 patients (72%) within 10 min. OH magnitude was significantly associated with disease severity (UMSARS I, II and IV), orthostatic symptoms (UMSARS I) and supine hypertension. OH severity was not associated with MSA subtype. Drug intake did not differ according to OH magnitude except for antihypertensive drugs being less frequently, and antihypotensive drugs more frequently, prescribed in severe OH. Conclusions: This is the largest study of OH in patients with MSA. Our data suggest that the sensitivity to pick up OH increases substantially by a prolonged 10 min orthostatic challenge. These results will help to improve OH management and the design of future clinical trials.Fil: Pavy Le Traon, Anne. University Hospital of Toulouse; Francia. Inserm; FranciaFil: Piedvache, A.. Université Paul Sabatier; FranciaFil: Pérez Lloret, Santiago. University Hospital of Toulouse; Francia. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Instituto de Investigaciones Biomédicas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas; ArgentinaFil: Calandra Buonara, G.. Università di Bologna; Italia. Istituto delle Scienze Neurologiche di Bologna; ItaliaFil: Cochen De Cock, V.. University Hospital of Toulouse; Francia. University of Montpellier; FranciaFil: Colosimo, C.. Sapienza Università di Roma; ItaliaFil: Cortelli, P.. Università di Bologna; Italia. Istituto delle Scienze Neurologiche di Bologna; ItaliaFil: Debs, R.. University Hospital of Toulouse; FranciaFil: Duerr, S.. Universidad de Innsbruck; AustriaFil: Fanciulli, A.. Universidad de Innsbruck; AustriaFil: Foubert Samier, A.. Centre Hospitalier Universitaire de Bordeaux; Francia. Universite de Bordeaux; FranciaFil: Gerdelat, Angela. University Hospital of Toulouse; FranciaFil: Gurevich, T.. Tel-Aviv University; IsraelFil: Krismer, F.. Universidad de Innsbruck; AustriaFil: Poewe, W.. Universidad de Innsbruck; AustriaFil: Tison, Francois. Universite de Bordeaux; Francia. Centre Hospitalier Universitaire de Bordeaux; FranciaFil: Tranchant, C.. University Hospital Hautepierre; FranciaFil: Wenning, G.. Universidad de Innsbruck; AustriaFil: Meissner, Wassilios G.. Universite de Bordeaux; Francia. Centre Hospitalier Universitaire de Bordeaux; FranciaFil: Rascol, Olivier. University Hospital of Toulouse; Franci

Moving glass theory of driven lattices with disorder

We study periodic structures, such as vortex lattices, moving in a random potential. As predicted in [T. Giamarchi, P. Le Doussal Phys. Rev. Lett. 76 3408 (1996)] the periodicity in the direction transverse to motion leads to a new class of driven systems: the Moving Glasses. We analyse using several RG techniques the properties at T=0 and $T>0$: (i) decay of translational long range order (ii) particles flow along static channels (iii) the channel pattern is highly correlated (iv) barriers to transverse motion. We demonstrate the existence of the ``transverse critical force'' at T=0. A ``static random force'' is shown to be generated by motion. Displacements grow logarithmically in $d=3$ and algebraically in $d=2$. The persistence of quasi long range translational order in $d=3$ at weak disorder, or large velocity leads to predict a topologically ordered ``Moving Bragg Glass''. This state continues the static Bragg glass and is stable at $T>0$, with non linear transverse response and linear asymptotic behavior. In $d=2$, or in $d=3$ at intermediate disorder, another moving glass exist (the Moving Transverse Glass) with smectic quasi order in the transverse direction. A phase diagram in $T$ force and disorder for static and moving structures is proposed. For correlated disorder we predict a ``moving Bose glass'' state with anisotropic transverse Meissner effect and transverse pinning. We discuss experimental consequences such as anomalous Hall effect in Wigner crystal and transverse critical current in vortex lattice.Comment: 74 pages, 27 figures, RevTe

Manin matrices and Talalaev's formula

We study special class of matrices with noncommutative entries and demonstrate their various applications in integrable systems theory. They appeared in Yu. Manin's works in 87-92 as linear homomorphisms between polynomial rings; more explicitly they read: 1) elements in the same column commute; 2) commutators of the cross terms are equal: $[M_{ij}, M_{kl}]=[M_{kj}, M_{il}]$ (e.g. $[M_{11}, M_{22}]=[M_{21}, M_{12}]$). We claim that such matrices behave almost as well as matrices with commutative elements. Namely theorems of linear algebra (e.g., a natural definition of the determinant, the Cayley-Hamilton theorem, the Newton identities and so on and so forth) holds true for them. On the other hand, we remark that such matrices are somewhat ubiquitous in the theory of quantum integrability. For instance, Manin matrices (and their q-analogs) include matrices satisfying the Yang-Baxter relation "RTT=TTR" and the so--called Cartier-Foata matrices. Also, they enter Talalaev's hep-th/0404153 remarkable formulas: $det(\partial_z-L_{Gaudin}(z))$, det(1-e^{-\p}T_{Yangian}(z)) for the "quantum spectral curve", etc. We show that theorems of linear algebra, after being established for such matrices, have various applications to quantum integrable systems and Lie algebras, e.g in the construction of new generators in $Z(U(\hat{gl_n}))$ (and, in general, in the construction of quantum conservation laws), in the Knizhnik-Zamolodchikov equation, and in the problem of Wick ordering. We also discuss applications to the separation of variables problem, new Capelli identities and the Langlands correspondence.Comment: 40 pages, V2: exposition reorganized, some proofs added, misprints e.g. in Newton id-s fixed, normal ordering convention turned to standard one, refs. adde

Change of dopamine receptor mRNA expression in lymphocyte of schizophrenic patients

BACKGROUND: Though the dysfunction of central dopaminergic system has been proposed, the etiology or pathogenesis of schizophrenia is still uncertain partly due to limited accessibility to dopamine receptor. The purpose of this study was to define whether or not the easily accessible dopamine receptors of peripheral lymphocytes can be the peripheral markers of schizophrenia. RESULTS: 44 drug-medicated schizophrenics for more than 3 years, 28 drug-free schizophrenics for more than 3 months, 15 drug-naïve schizophrenic patients, and 31 healthy persons were enrolled. Sequential reverse transcription and quantitative polymerase chain reaction of the mRNA were used to investigate the expression of D3 and D5 dopamine receptors in peripheral lymphocytes. The gene expression of dopamine receptors was compared in each group. After taking antipsychotics in drug-free and drug-naïve patients, the dopamine receptors of peripheral lymphocytes were sequentially studied 2nd week and 8th week after medication. In drug-free schizophrenics, D3 dopamine receptor mRNA expression of peripheral lymphocytes significantly increased compared to that of controls and drug-medicated schizophrenics, and D5 dopamine receptor mRNA expression increased compared to that of drug-medicated schizophrenics. After taking antipsychotics, mRNA of dopamine receptors peaked at 2(nd) week, after which it decreases but the level was above baseline one at 8(th) week. Drug-free and drug-naïve patients were divided into two groups according to dopamine receptor expression before medications, and the group of patients with increased dopamine receptor expression had more severe psychiatric symptoms. CONCLUSIONS: These results reveal that the molecular biologically-determined dopamine receptors of peripheral lymphocytes are reactive, and that increased expression of dopamine receptor in peripheral lymphocyte has possible clinical significance for subgrouping of schizophrenis

Agonist-induced internalisation of the glucagon-like peptide-1 receptor is mediated by the Gαq pathway

The glucagon like peptide-1 receptor (GLP-1R) is a G-protein coupled receptor (GPCR) and an important target in the treatment of type 2 diabetes mellitus (T2DM). Upon stimulation with agonist, the GLP-1R signals through both Gαs and Gαq coupled pathways to stimulate insulin secretion. The agonist induced GLP-1R internalisation has recently been shown to be important for insulin secretion. However, the molecular mechanisms underlying GLP-1R internalisation remain unknown. The aim of this study was to determine the role of GLP-1R downstream signalling pathways in its internalisation. Agonist induced human GLP-1R (hGLP-1R) internalisation and activity were examined using a number of techniques including immunoblotting, ELISA, immunofluorescence, and luciferase assays to determine cAMP production, intracellular Ca2+ accumulation and ERK phosphorylation. Agonist induced hGLP-1R internalisation is dependent on caveolin-1 and dynamin. Inhibition of the Gαq pathway but not the Gαs pathway affected hGLP-1R internalisation. Consistent with this, hGLP-1R mutant T149 M and small molecule agonists (compound 2 and compound B), which activate only the Gαs pathway, failed to induce internalisation of the receptor. Chemical inhibitors of the Gαq pathway, PKC and ERK phosphorylation significantly reduced agonist induced hGLP-1R internalisation. These inhibitors also suppressed agonist induced ERK1/2 phosphorylation demonstrating that the phosphorylated ERK acts downstream of the Gαq pathway in the hGLP-1R internalisation. In summary, agonist induced hGLP-1R internalisation is mediated by the Gαq pathway. The internalised hGLP-1R stimulates insulin secretion from pancreatic β-cells, indicating the importance of GLP-1 internalisation for insulin secretion

Mechanistic Models of Biofilm Growth in Porous Media

Nondestructive acoustics methods can be used to monitor in situ biofilm growth in porous media. In practice, however, acoustic methods remain underutilized due to the lack of models that can translate acoustic data into rock properties in the context of biofilm. In this paper we present mechanistic models of biofilm growth in porous media. The models are used to quantitatively interpret arrival times and amplitudes recorded in the 29 day long Davis et al. (2010) physical scale biostimulation experiment in terms of biofilm morphologies and saturation. The model pivots on addressing the sediment elastic behavior using the lower Hashin-Shtrikman bounds for grain mixing and Gassmann substitution for fluid saturation. The time-lapse P wave velocity (VP; a function of arrival times) is explained by a combination of two rock models (morphologies); load bearing which assumes the biofilm as an additional mineral in the rock matrix and pore filling which assumes the biofilm as an additional fluid phase in the pores. The time-lapse attenuation (QP-1; a function of amplitudes), on the other hand, can be explained adequately in two ways; first, through squirt flow where energy is lost from relative motion between rock matrix and pore fluid, and second, through an empirical function of porosity (φ), permeability (κ), and grain size. The squirt flow model-fitting results in higher internal φ (7% versus 5%) and more oblate pores (0.33 versus 0.67 aspect ratio) for the load-bearing morphology versus the pore-filling morphology. The empirical model-fitting results in up to 10% increase in κ at the initial stages of the load-bearing morphology. The two morphologies which exhibit distinct mechanical and hydraulic behavior could be a function of pore throat size. The biofilm mechanistic models developed in this study can be used for the interpretation of seismic data critical for the evaluation of biobarriers in bioremediation, microbial enhanced oil recovery, and CO2 sequestration