TY - JOUR AB - Considering a continuous self-map and the induced endomorphism on homology, we study the eigenvalues and eigenspaces of the latter. Taking a filtration of representations, we define the persistence of the eigenspaces, effectively introducing a hierarchical organization of the map. The algorithm that computes this information for a finite sample is proved to be stable, and to give the correct answer for a sufficiently dense sample. Results computed with an implementation of the algorithm provide evidence of its practical utility. AU - Edelsbrunner, Herbert AU - Jablonski, Grzegorz AU - Mrozek, Marian ID - 2035 IS - 5 JF - Foundations of Computational Mathematics TI - The persistent homology of a self-map VL - 15 ER - TY - JOUR AB - Opacity is a generic security property, that has been defined on (non-probabilistic) transition systems and later on Markov chains with labels. For a secret predicate, given as a subset of runs, and a function describing the view of an external observer, the value of interest for opacity is a measure of the set of runs disclosing the secret. We extend this definition to the richer framework of Markov decision processes, where non-deterministicchoice is combined with probabilistic transitions, and we study related decidability problems with partial or complete observation hypotheses for the schedulers. We prove that all questions are decidable with complete observation and ω-regular secrets. With partial observation, we prove that all quantitative questions are undecidable but the question whether a system is almost surely non-opaquebecomes decidable for a restricted class of ω-regular secrets, as well as for all ω-regular secrets under finite-memory schedulers. AU - Bérard, Béatrice AU - Chatterjee, Krishnendu AU - Sznajder, Nathalie ID - 2034 IS - 1 JF - Information Processing Letters TI - Probabilistic opacity for Markov decision processes VL - 115 ER - TY - JOUR AB - We study the spectrum of a large system of N identical bosons interacting via a two-body potential with strength 1/N. In this mean-field regime, Bogoliubov's theory predicts that the spectrum of the N-particle Hamiltonian can be approximated by that of an effective quadratic Hamiltonian acting on Fock space, which describes the fluctuations around a condensed state. Recently, Bogoliubov's theory has been justified rigorously in the case that the low-energy eigenvectors of the N-particle Hamiltonian display complete condensation in the unique minimizer of the corresponding Hartree functional. In this paper, we shall justify Bogoliubov's theory for the high-energy part of the spectrum of the N-particle Hamiltonian corresponding to (non-linear) excited states of the Hartree functional. Moreover, we shall extend the existing results on the excitation spectrum to the case of non-uniqueness and/or degeneracy of the Hartree minimizer. In particular, the latter covers the case of rotating Bose gases, when the rotation speed is large enough to break the symmetry and to produce multiple quantized vortices in the Hartree minimizer. AU - Nam, Phan AU - Seiringer, Robert ID - 2085 IS - 2 JF - Archive for Rational Mechanics and Analysis TI - Collective excitations of Bose gases in the mean-field regime VL - 215 ER - TY - JOUR AB - We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014). AU - Erdös, László AU - Knowles, Antti ID - 2166 IS - 3 JF - Communications in Mathematical Physics TI - The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case VL - 333 ER - TY - JOUR AB - Linearizability of concurrent data structures is usually proved by monolithic simulation arguments relying on the identification of the so-called linearization points. Regrettably, such proofs, whether manual or automatic, are often complicated and scale poorly to advanced non-blocking concurrency patterns, such as helping and optimistic updates. In response, we propose a more modular way of checking linearizability of concurrent queue algorithms that does not involve identifying linearization points. We reduce the task of proving linearizability with respect to the queue specification to establishing four basic properties, each of which can be proved independently by simpler arguments. As a demonstration of our approach, we verify the Herlihy and Wing queue, an algorithm that is challenging to verify by a simulation proof. AU - Chakraborty, Soham AU - Henzinger, Thomas A AU - Sezgin, Ali AU - Vafeiadis, Viktor ID - 1832 IS - 1 JF - Logical Methods in Computer Science TI - Aspect-oriented linearizability proofs VL - 11 ER - TY - JOUR AB - A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. Finite-valued constraint languages contain functions that take on rational costs and general-valued constraint languages contain functions that take on rational or infinite costs. An instance of the problem is specified by a sum of functions from the language with the goal to minimise the sum. This framework includes and generalises well-studied constraint satisfaction problems (CSPs) and maximum constraint satisfaction problems (Max-CSPs). Our main result is a precise algebraic characterisation of valued constraint languages whose instances can be solved exactly by the basic linear programming relaxation (BLP). For a general-valued constraint language Γ, BLP is a decision procedure for Γ if and only if Γ admits a symmetric fractional polymorphism of every arity. For a finite-valued constraint language Γ, BLP is a decision procedure if and only if Γ admits a symmetric fractional polymorphism of some arity, or equivalently, if Γ admits a symmetric fractional polymorphism of arity 2. Using these results, we obtain tractability of several novel and previously widely-open classes of VCSPs, including problems over valued constraint languages that are: (1) submodular on arbitrary lattices; (2) bisubmodular (also known as k-submodular) on arbitrary finite domains; (3) weakly (and hence strongly) tree-submodular on arbitrary trees. AU - Kolmogorov, Vladimir AU - Thapper, Johan AU - Živný, Stanislav ID - 2271 IS - 1 JF - SIAM Journal on Computing TI - The power of linear programming for general-valued CSPs VL - 44 ER - TY - JOUR AB - For suitable pairs of diagonal quadratic forms in eight variables we use the circle method to investigate the density of simultaneous integer solutions and relate this to the problem of estimating linear correlations among sums of two squares. AU - Timothy Browning AU - Munshi, Ritabrata ID - 257 IS - 4 JF - Forum Mathematicum TI - Pairs of diagonal quadratic forms and linear correlations among sums of two squares VL - 27 ER - TY - CHAP AB - Given a number field k and a projective algebraic variety X defined over k, the question of whether X contains a k-rational point is both very natural and very difficult. In the event that the set X(k) of k-rational points is not empty, one can also ask how the points of X(k) are distributed. Are they dense in X under the Zariski topology? Are they dense in the set. AU - Browning, Timothy D ID - 258 T2 - Arithmetic and Geometry TI - A survey of applications of the circle method to rational points ER - TY - JOUR AB - The Hasse principle and weak approximation is established for non-singular cubic hypersurfaces X over the function field AU - Timothy Browning AU - Vishe, Pankaj ID - 259 IS - 3 JF - Geometric and Functional Analysis TI - Rational points on cubic hypersurfaces over F_q(t) VL - 25 ER - TY - JOUR AB - We consider Markov decision processes (MDPs) with specifications given as Büchi (liveness) objectives, and examine the problem of computing the set of almost-sure winning vertices such that the objective can be ensured with probability 1 from these vertices. We study for the first time the average-case complexity of the classical algorithm for computing the set of almost-sure winning vertices for MDPs with Büchi objectives. Our contributions are as follows: First, we show that for MDPs with constant out-degree the expected number of iterations is at most logarithmic and the average-case running time is linear (as compared to the worst-case linear number of iterations and quadratic time complexity). Second, for the average-case analysis over all MDPs we show that the expected number of iterations is constant and the average-case running time is linear (again as compared to the worst-case linear number of iterations and quadratic time complexity). Finally we also show that when all MDPs are equally likely, the probability that the classical algorithm requires more than a constant number of iterations is exponentially small. AU - Chatterjee, Krishnendu AU - Joglekar, Manas AU - Shah, Nisarg ID - 1598 IS - 3 JF - Theoretical Computer Science TI - Average case analysis of the classical algorithm for Markov decision processes with Büchi objectives VL - 573 ER - TY - JOUR AB - We consider the problem of deciding whether the persistent homology group of a simplicial pair (K,L) can be realized as the homology H∗(X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard. AU - Attali, Dominique AU - Bauer, Ulrich AU - Devillers, Olivier AU - Glisse, Marc AU - Lieutier, André ID - 1805 IS - 8 JF - Computational Geometry: Theory and Applications TI - Homological reconstruction and simplification in R3 VL - 48 ER - TY - JOUR AB - We present a hybrid intercalation battery based on a sodium/magnesium (Na/Mg) dual salt electrolyte, metallic magnesium anode, and a cathode based on FeS2 nanocrystals (NCs). Compared to lithium or sodium, metallic magnesium anode is safer due to dendrite-free electroplating and offers extremely high volumetric (3833 mAh cm-3) and gravimetric capacities (2205 mAh g-1). Na-ion cathodes, FeS2 NCs in the present study, may serve as attractive alternatives to Mg-ion cathodes due to the higher voltage of operation and fast, highly reversible insertion of Na-ions. In this proof-of-concept study, electrochemical cycling of the Na/Mg hybrid battery was characterized by high rate capability, high Coulombic efficiency of 99.8%, and high energy density. In particular, with an average discharge voltage of ∼1.1 V and a cathodic capacity of 189 mAh g-1 at a current of 200 mA g-1, the presented Mg/FeS2 hybrid battery delivers energy densities of up to 210 Wh kg-1, comparable to commercial Li-ion batteries and approximately twice as high as state-of-the-art Mg-ion batteries based on Mo6S8 cathodes. Further significant gains in the energy density are expected from the development of Na/Mg electrolytes with a broader electrochemical stability window. Fully based on Earth-abundant elements, hybrid Na-Mg batteries are highly promising for large-scale stationary energy storage. AU - Walter, Marc AU - Kravchyk, Kostiantyn AU - Ibáñez, Maria AU - Kovalenko, Maksym ID - 333 IS - 21 JF - Chemistry of Materials TI - Efficient and inexpensive sodium magnesium hybrid battery VL - 27 ER - TY - JOUR AB - A simple and effective method to introduce precise amounts of doping in nanomaterials produced from the bottom-up assembly of colloidal nanoparticles (NPs) is described. The procedure takes advantage of a ligand displacement step to incorporate controlled concentrations of halide ions while removing carboxylic acids from the NP surface. Upon consolidation of the NPs into dense pellets, halide ions diffuse within the crystal structure, doping the anion sublattice and achieving n-type electrical doping. Through the characterization of the thermoelectric properties of nanocrystalline PbS, we demonstrate this strategy to be effective to control charge transport properties on thermoelectric nanomaterials assembled from NP building blocks. This approach is subsequently extended to PbTexSe1-x@PbS core-shell NPs, where a significant enhancement of the thermoelectric figure of merit is achieved. AU - Ibáñez, Maria AU - Korkosz, Rachel AU - Luo, Zhishan AU - Riba, Pau AU - Cadavid, Doris AU - Ortega, Silvia AU - Cabot, Andreu AU - Kanatzidis, Mercouri ID - 354 IS - 12 JF - Journal of the American Chemical Society TI - Electron doping in bottom up engineered thermoelectric nanomaterials through HCl mediated ligand displacement VL - 137 ER - TY - JOUR AB - A cation exchange-based route was used to produce Cu2ZnSnS4 (CZTS)-Ag2S nanoparticles with controlled composition. We report a detailed study of the formation of such CZTS-Ag2S nanoheterostructures and of their photocatalytic properties. When compared to pure CZTS, the use of nanoscale p-n heterostructures as light absorbers for photocatalytic water splitting provides superior photocurrents. We associate this experimental fact to a higher separation efficiency of the photogenerated electron-hole pairs. We believe this and other type-II nanoheterostructures will open the door to the use of CZTS, with excellent light absorption properties and made of abundant and environmental friendly elements, to the field of photocatalysis. AU - Yu, Xuelian AU - Liu, Jingjing AU - Genç, Aziz AU - Ibáñez, Maria AU - Luo, Zhishan AU - Shavel, Alexey AU - Arbiol, Jordi AU - Zhang, Guangjin AU - Zhang, Yihe AU - Cabot, Andreu ID - 360 IS - 38 JF - Langmuir TI - Cu2ZnSnS4-Ag2S nanoscale p-n heterostructures as sensitizers for photoelectrochemical water splitting VL - 31 ER - TY - JOUR AB - Monodisperse Pd2Sn nanorods with tuned size and aspect ratio were prepared by co-reduction of metal salts in the presence of trioctylphosphine, amine, and chloride ions. Asymmetric Pd2Sn nanostructures were achieved by the selective desorption of a surfactant mediated by chlorine ions. A preliminary evaluation of the geometry influence on catalytic properties evidenced Pd2Sn nanorods to have improved catalytic performance. In view of these results, Pd2Sn nanorods were also evaluated for water denitration. AU - Lu, Zhishan AU - Ibáñez, Maria AU - Antolín, Ana AU - Genç, Aziz AU - Shavel, Alexey AU - Contreras, Sandra AU - Medina, Francesc AU - Arbiol, Jordi AU - Cabot, Andreu ID - 362 IS - 13 JF - Langmuir TI - Size and aspect ratio control of Pd inf 2 inf Sn nanorods and their water denitration properties VL - 31 ER - TY - JOUR AB - We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games. AU - Chatterjee, Krishnendu AU - Doyen, Laurent AU - Gimbert, Hugo AU - Henzinger, Thomas A ID - 1731 IS - 12 JF - Information and Computation TI - Randomness for free VL - 245 ER - TY - JOUR AB - A cation exchange-based route was used to produce Cu2ZnSnS4 (CZTS)-Ag2S nanoparticles with controlled composition. We report a detailed study of the formation of such CZTS-Ag2S nanoheterostructures and of their photocatalytic properties. When compared to pure CZTS, the use of nanoscale p-n heterostructures as light absorbers for photocatalytic water splitting provides superior photocurrents. We associate this experimental fact to a higher separation efficiency of the photogenerated electron-hole pairs. We believe this and other type-II nanoheterostructures will open the door to the use of CZTS, with excellent light absorption properties and made of abundant and environmental friendly elements, to the field of photocatalysis. AU - Yu, Xuelian AU - Liu, Jingjing AU - Genç, Aziz AU - Ibáñez, Maria AU - Luo, Zhishan AU - Shavel, Alexey AU - Arbiol, Jordi AU - Zhang, Guangjin AU - Zhang, Yihe AU - Cabot, Andreu ID - 334 IS - 38 JF - Langmuir TI - Cu2ZnSnS4–Ag2S Nanoscale p–n heterostructures as sensitizers for photoelectrochemical water splitting VL - 31 ER - TY - JOUR AB - We report the synthesis and photocatalytic and magnetic characterization of colloidal nanoheterostructures formed by combining a Pt-based magnetic metal alloy (PtCo, PtNi) with Cu2ZnSnS4 (CZTS). While CZTS is one of the main candidate materials for solar energy conversion, the introduction of a Pt-based alloy on its surface strongly influences its chemical and electronic properties, ultimately determining its functionality. In this regard, up to a 15-fold increase of the photocatalytic hydrogen evolution activity was obtained with CZTS–PtCo when compared with CZTS. Furthermore, two times higher hydrogen evolution rates were obtained for CZTS–PtCo when compared with CZTS–Pt, in spite of the lower precious metal loading of the former. Besides, the magnetic properties of the PtCo nanoparticles attached to the CZTS nanocrystals were retained in the heterostructures, which could facilitate catalyst purification and recovery for its posterior recycling and/or reutilization. AU - Yu, Xuelian AU - An, Xiaoqiang AU - Genç, Aziz AU - Ibáñez, Maria AU - Arbiol, Jordi AU - Zhang, Yihe AU - Cabot, Andreu ID - 361 IS - 38 JF - Journal of Physical Chemistry C TI - Cu2ZnSnS4–PtM (M = Co, Ni) nanoheterostructures for photocatalytic hydrogen evolution VL - 119 ER - TY - JOUR AB - The traditional synthesis question given a specification asks for the automatic construction of a system that satisfies the specification, whereas often there exists a preference order among the different systems that satisfy the given specification. Under a probabilistic assumption about the possible inputs, such a preference order is naturally expressed by a weighted automaton, which assigns to each word a value, such that a system is preferred if it generates a higher expected value. We solve the following optimal synthesis problem: given an omega-regular specification, a Markov chain that describes the distribution of inputs, and a weighted automaton that measures how well a system satisfies the given specification under the input assumption, synthesize a system that optimizes the measured value. For safety specifications and quantitative measures that are defined by mean-payoff automata, the optimal synthesis problem reduces to finding a strategy in a Markov decision process (MDP) that is optimal for a long-run average reward objective, which can be achieved in polynomial time. For general omega-regular specifications along with mean-payoff automata, the solution rests on a new, polynomial-time algorithm for computing optimal strategies in MDPs with mean-payoff parity objectives. Our algorithm constructs optimal strategies that consist of two memoryless strategies and a counter. The counter is in general not bounded. To obtain a finite-state system, we show how to construct an ε-optimal strategy with a bounded counter, for all ε > 0. Furthermore, we show how to decide in polynomial time if it is possible to construct an optimal finite-state system (i.e., a system without a counter) for a given specification. We have implemented our approach and the underlying algorithms in a tool that takes qualitative and quantitative specifications and automatically constructs a system that satisfies the qualitative specification and optimizes the quantitative specification, if such a system exists. We present some experimental results showing optimal systems that were automatically generated in this way. AU - Chatterjee, Krishnendu AU - Henzinger, Thomas A AU - Jobstmann, Barbara AU - Singh, Rohit ID - 1856 IS - 1 JF - Journal of the ACM TI - Measuring and synthesizing systems in probabilistic environments VL - 62 ER - TY - JOUR AB - We use ultrafast optical spectroscopy to observe binding of charged single-particle excitations (SE) in the magnetically frustrated Mott insulator Na2IrO3. Above the antiferromagnetic ordering temperature (TN) the system response is due to both Hubbard excitons (HE) and their constituent unpaired SE. The SE response becomes strongly suppressed immediately below TN. We argue that this increase in binding energy is due to a unique interplay between the frustrated Kitaev and the weak Heisenberg-type ordering term in the Hamiltonian, mediating an effective interaction between the spin-singlet SE. This interaction grows with distance causing the SE to become trapped in the HE, similar to quark confinement inside hadrons. This binding of charged particles, induced by magnetic ordering, is a result of a confinement-deconfinement transition of spin excitations. This observation provides evidence for spin liquid type behavior which is expected in Na2IrO3. AU - Alpichshev, Zhanybek AU - Mahmood, Fahad AU - Cao, Gang AU - Gedik, Nuh ID - 388 IS - 1 JF - Physical Review Letters TI - Confinement deconfinement transition as an indication of spin liquid type behavior in Na2IrO3 VL - 114 ER -