Semi-supervised Learning based on Distributionally Robust Optimization

We propose a novel method for semi-supervised learning (SSL) based on data-driven distributionally robust optimization (DRO) using optimal transport metrics. Our proposed method enhances generalization error by using the unlabeled data to restrict the support of the worst case distribution in our DRO formulation. We enable the implementation of our DRO formulation by proposing a stochastic gradient descent algorithm which allows to easily implement the training procedure. We demonstrate that our Semi-supervised DRO method is able to improve the generalization error over natural supervised procedures and state-of-the-art SSL estimators. Finally, we include a discussion on the large sample behavior of the optimal uncertainty region in the DRO formulation. Our discussion exposes important aspects such as the role of dimension reduction in SSL

Periodic alternating 0,π0,\pi-junction structures as realization of ϕ\phi-Josephson junctions

We consider the properties of a periodic structure consisting of small alternating 0- and pi- Josephson junctions. We show that depending on the relation between the lengths of the individual junctions, this system can be either in the homogeneous or in the phase-modulated state. The modulated phase appears via a second order phase transition when the mismatch between the lengths of the individual junctions exceeds the critical value. The screening length diverges at the transition point. In the modulated state, the equilibrium phase difference in the structure can take any value from -pi to pi (phi-junction). The current-phase relation in this structure has very unusual shape with two maxima. As a consequence, the field dependence of the critical current in a small structure is very different from the standard Fraunhofer dependence. The Josephson vortex in a long structure carries partial magnetic flux, which is determined by the equilibrium phase.Comment: 4 pages, 3 figues, submitted to Phys. Rev.

The leading Ruelle resonances of chaotic maps

The leading Ruelle resonances of typical chaotic maps, the perturbed cat map and the standard map, are calculated by variation. It is found that, excluding the resonance associated with the invariant density, the next subleading resonances are, approximately, the roots of the equation $z^4=\gamma$, where $\gamma$ is a positive number which characterizes the amount of stochasticity of the map. The results are verified by numerical computations, and the implications to the form factor of the corresponding quantum maps are discussed.Comment: 5 pages, 4 figures included. To appear in Phys. Rev.

Simple heuristics for the assembly line worker assignment and balancing problem

We propose simple heuristics for the assembly line worker assignment and balancing problem. This problem typically occurs in assembly lines in sheltered work centers for the disabled. Different from the classical simple assembly line balancing problem, the task execution times vary according to the assigned worker. We develop a constructive heuristic framework based on task and worker priority rules defining the order in which the tasks and workers should be assigned to the workstations. We present a number of such rules and compare their performance across three possible uses: as a stand-alone method, as an initial solution generator for meta-heuristics, and as a decoder for a hybrid genetic algorithm. Our results show that the heuristics are fast, they obtain good results as a stand-alone method and are efficient when used as a initial solution generator or as a solution decoder within more elaborate approaches.Comment: 18 pages, 1 figur

Explicit CP violation in the Dine-Seiberg-Thomas model

The possibility of explicit CP violation is studied in a supersymmetric model proposed by Dine, Seiberg, and Thomas, with two effective dimension-five operators. The explicit CP violation may be triggered by complex phases in the coefficients for the dimension-five operators in the Higgs potential, and by a complex phase in the scalar top quark masses. Although the scenario of explicit CP violation is found to be inconsistent with the experimental data at LEP2 at the tree level, it may be possible at the one-loop level. For a reasonable parameter space, the masses of the neutral Higgs bosons and their couplings to a pair of $Z$ bosons are consistent with the LEP2 data, at the one-loop level.Comment: 5 pages, 2 figure

Topology, Entropy and Witten Index of Dilaton Black Holes

We have found that for extreme dilaton black holes an inner boundary must be introduced in addition to the outer boundary to give an integer value to the Euler number. The resulting manifolds have (if one identifies imaginary time) topology $S^1 \times R \times S^2$ and Euler number $\chi = 0$ in contrast to the non-extreme case with $\chi=2$. The entropy of extreme $U(1)$ dilaton black holes is already known to be zero. We include a review of some recent ideas due to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black holes as having an inner boundary, we conclude that the entropy of {\sl all} extreme black holes, including $[U(1)]^2$ black holes, vanishes. We discuss the relevance of this to the vanishing of quantum corrections and the idea that the functional integral for extreme holes gives a Witten Index. We have studied also the topology of ``moduli space'' of multi black holes. The quantum mechanics on black hole moduli spaces is expected to be supersymmetric despite the fact that they are not HyperK\"ahler since the corresponding geometry has torsion unlike the BPS monopole case. Finally, we describe the possibility of extreme black hole fission for states with an energy gap. The energy released, as a proportion of the initial rest mass, during the decay of an electro-magnetic black hole is 300 times greater than that released by the fission of an ${}^{235} U$ nucleus.Comment: 51 pages, 4 figures, LaTeX. Considerably extended version. New sections include discussion of the Witten index, topology of the moduli space, black hole sigma model, and black hole fission with huge energy releas

Succinct Representation of Codes with Applications to Testing

Motivated by questions in property testing, we search for linear error-correcting codes that have the "single local orbit" property: i.e., they are specified by a single local constraint and its translations under the symmetry group of the code. We show that the dual of every "sparse" binary code whose coordinates are indexed by elements of F_{2^n} for prime n, and whose symmetry group includes the group of non-singular affine transformations of F_{2^n} has the single local orbit property. (A code is said to be "sparse" if it contains polynomially many codewords in its block length.) In particular this class includes the dual-BCH codes for whose duals (i.e., for BCH codes) simple bases were not known. Our result gives the first short (O(n)-bit, as opposed to the natural exp(n)-bit) description of a low-weight basis for BCH codes. The interest in the "single local orbit" property comes from the recent result of Kaufman and Sudan (STOC 2008) that shows that the duals of codes that have the single local orbit property under the affine symmetry group are locally testable. When combined with our main result, this shows that all sparse affine-invariant codes over the coordinates F_{2^n} for prime n are locally testable. If, in addition to n being prime, if 2^n-1 is also prime (i.e., 2^n-1 is a Mersenne prime), then we get that every sparse cyclic code also has the single local orbit. In particular this implies that BCH codes of Mersenne prime length are generated by a single low-weight codeword and its cyclic shifts

The STAR Time Projection Chamber: A Unique Tool for Studying High Multiplicity Events at RHIC

The STAR Time Projection Chamber (TPC) is used to record collisions at the Relativistic Heavy Ion Collider (RHIC). The TPC is the central element in a suite of detectors that surrounds the interaction vertex. The TPC provides complete coverage around the beam-line, and provides complete tracking for charged particles within +- 1.8 units of pseudo-rapidity of the center-of-mass frame. Charged particles with momenta greater than 100 MeV/c are recorded. Multiplicities in excess of 3,000 tracks per event are routinely reconstructed in the software. The TPC measures 4 m in diameter by 4.2 m long, making it the largest TPC in the world.Comment: 28 pages, 11 figure

Long-term risk of adverse outcomes according to atrial fibrillation type.

Sustained forms of atrial fibrillation (AF) may be associated with a higher risk of adverse outcomes, but few if any long-term studies took into account changes of AF type and co-morbidities over time. We prospectively followed 3843 AF patients and collected information on AF type and co-morbidities during yearly follow-ups. The primary outcome was a composite of stroke or systemic embolism (SE). Secondary outcomes included myocardial infarction, hospitalization for congestive heart failure (CHF), bleeding and all-cause mortality. Multivariable adjusted Cox proportional hazards models with time-varying covariates were used to compare hazard ratios (HR) according to AF type. At baseline 1895 (49%), 1046 (27%) and 902 (24%) patients had paroxysmal, persistent and permanent AF and 3234 (84%) were anticoagulated. After a median (IQR) follow-up of 3.0 (1.9; 4.2) years, the incidence of stroke/SE was 1.0 per 100 patient-years. The incidence of myocardial infarction, CHF, bleeding and all-cause mortality was 0.7, 3.0, 2.9 and 2.7 per 100 patient-years, respectively. The multivariable adjusted (a) HRs (95% confidence interval) for stroke/SE were 1.13 (0.69; 1.85) and 1.27 (0.83; 1.95) for time-updated persistent and permanent AF, respectively. The corresponding aHRs were 1.23 (0.89, 1.69) and 1.45 (1.12; 1.87) for all-cause mortality, 1.34 (1.00; 1.80) and 1.30 (1.01; 1.67) for CHF, 0.91 (0.48; 1.72) and 0.95 (0.56; 1.59) for myocardial infarction, and 0.89 (0.70; 1.14) and 1.00 (0.81; 1.24) for bleeding. In this large prospective cohort of AF patients, time-updated AF type was not associated with incident stroke/SE