Daily Papers

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient (epsilon,delta)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with k nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) epsilon-DP algorithm would result in substantial error.

The problem of attributing a deep network's prediction to its input/base features is well-studied. We introduce the notion of conductance to extend the notion of attribution to the understanding the importance of hidden units. Informally, the conductance of a hidden unit of a deep network is the flow of attribution via this hidden unit. We use conductance to understand the importance of a hidden unit to the prediction for a specific input, or over a set of inputs. We evaluate the effectiveness of conductance in multiple ways, including theoretical properties, ablation studies, and a feature selection task. The empirical evaluations are done using the Inception network over ImageNet data, and a sentiment analysis network over reviews. In both cases, we demonstrate the effectiveness of conductance in identifying interesting insights about the internal workings of these networks.

We use the AdS/CFT correspondence to compute the conductivity of massive N=2 hypermultiplet fields at finite baryon number density in an N=4 SU(N_c) super-Yang-Mills theory plasma in the large N_c, large 't Hooft coupling limit. The finite baryon density provides charge carriers analogous to electrons in a metal. An external electric field then induces a finite current which we determine directly. Our result for the conductivity is good for all values of the mass, external field and density, modulo statements about the yet-incomplete phase diagram. In the appropriate limits it agrees with known results obtained from analyzing small fluctuations around equilibrium. For large mass, where we expect a good quasi-particle description, we compute the drag force on the charge carriers and find that the answer is unchanged from the zero density case. Our method easily generalizes to a wide class of systems of probe branes in various backgrounds.

We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (DC) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles.

We continue our analysis on conductivity in the anisotropic background by employing the D-brane probe technique, where the D-branes play the role of charge carriers. The DC and AC conductivity for massless charge carriers are obtained analytically, while interesting curves for the AC conductivity are also plotted. For massive charge carriers, we calculate the DC and AC conductivities in the dilute limit and we fix the parameters in the Einstein-Maxwell-dilaton theory so that the background exhibits the same scaling behaviors as those for real-world strange metals. The DC conductivity at finite density is also computed.

We study a new connection between a technical measure called mu-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of mu-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal mu-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

We study charged dilaton black branes in AdS_4. Our system involves a dilaton phi coupled to a Maxwell field F_{munu} with dilaton-dependent gauge coupling, {1over g^2} = f^2(phi). First, we find the solutions for extremal and near extremal branes through a combination of analytical and numerical techniques. The near horizon geometries in the simplest cases, where f(phi) = e^{alphaphi}, are Lifshitz-like, with a dynamical exponent z determined by alpha. The black hole thermodynamics varies in an interesting way with alpha, but in all cases the entropy is vanishing and the specific heat is positive for the near extremal solutions. We then compute conductivity in these backgrounds. We find that somewhat surprisingly, the AC conductivity vanishes like omega^2 at T=0 independent of alpha. We also explore the charged black brane physics of several other classes of gauge-coupling functions f(phi). In addition to possible applications in AdS/CMT, the extremal black branes are of interest from the point of view of the attractor mechanism. The near horizon geometries for these branes are universal, independent of the asymptotic values of the moduli, and describe generic classes of endpoints for attractor flows which are different from AdS_2times R^2.

Since the mid-eighties there has been an accumulation of metallic materials whose thermodynamic and transport properties differ significantly from those predicted by Fermi liquid theory. Examples of these so-called non-Fermi liquids include the strange metal phase of high transition temperature cuprates, and heavy fermion systems near a quantum phase transition. We report on a class of non-Fermi liquids discovered using gauge/gravity duality. The low energy behavior of these non-Fermi liquids is shown to be governed by a nontrivial infrared (IR) fixed point which exhibits nonanalytic scaling behavior only in the temporal direction. Within this class we find examples whose single-particle spectral function and transport behavior resemble those of strange metals. In particular, the contribution from the Fermi surface to the conductivity is inversely proportional to the temperature. In our treatment these properties can be understood as being controlled by the scaling dimension of the fermion operator in the emergent IR fixed point.

One way to model the strange metal phase of certain materials is via a holographic description in terms of probe D-branes in a Lifshitz spacetime, characterised by a dynamical exponent z. The background geometry is dual to a strongly-interacting quantum critical theory while the probe D-branes are dual to a finite density of charge carriers that can exhibit the characteristic properties of strange metals. We compute holographically the low-frequency and low-momentum form of the charge density and current retarded Green's functions in these systems for massless charge carriers. The results reveal a quasi-particle excitation when z<2, which in analogy with Landau Fermi liquids we call zero sound. The real part of the dispersion relation depends on momentum k linearly, while the imaginary part goes as k^2/z. When z is greater than or equal to 2 the zero sound is not a well-defined quasi-particle. We also compute the frequency-dependent conductivity in arbitrary spacetime dimensions. Using that as a measure of the charge current spectral function, we find that the zero sound appears only when the spectral function consists of a single delta function at zero frequency.

Conventional semiconductor-based integrated circuits are gradually approaching fundamental scaling limits. Many prospective solutions have recently emerged to supplement or replace both the technology on which basic devices are built and the architecture of data processing. Neuromorphic circuits are a promising approach to computing where techniques used by the brain to achieve high efficiency are exploited. Many existing neuromorphic circuits rely on unconventional and useful properties of novel technologies to better mimic the operation of the brain. One such technology is single flux quantum (SFQ) logic -- a cryogenic superconductive technology in which the data are represented by quanta of magnetic flux (fluxons) produced and processed by Josephson junctions embedded within inductive loops. The movement of a fluxon within a circuit produces a quantized voltage pulse (SFQ pulse), resembling a neuronal spiking event. These circuits routinely operate at clock frequencies of tens to hundreds of gigahertz, making SFQ a natural technology for processing high frequency pulse trains. Prior proposals for SFQ neural networks often require energy-expensive fluxon conversions, involve heterogeneous technologies, or exclusively focus on device level behavior. In this paper, a design methodology for deep single flux quantum neuromorphic networks is presented. Synaptic and neuronal circuits based on SFQ technology are presented and characterized. Based on these primitives, a deep neuromorphic XOR network is evaluated as a case study, both at the architectural and circuit levels, achieving wide classification margins. The proposed methodology does not employ unconventional superconductive devices or semiconductor transistors. The resulting networks are tunable by an external current, making this proposed system an effective approach for scalable cryogenic neuromorphic computing.

We establish, in general terms, the conditions to be satisfied by a time-fractional approach formulation of the Poisson-Nernst-Planck model in order to guarantee that the total current across the sample be solenoidal, as required by the Maxwell equation. Only in this case the electric impedance of a cell can be determined as the ratio between the applied difference of potential and the current across the cell. We show that in the case of anomalous diffusion, the model predicts for the electric impedance of the cell a constant phase element behaviour in the low frequency region. In the parametric curve of the reactance versus the resistance, the slope coincides with the order of the fractional time derivative.

Probe branes with finite worldvolume electric flux in the background created by a stack of Dp branes describe holographically strongly interacting fundamental matter at finite density. We identify two quantities whose leading low temperature behavior is independent of the dimensionality of the probe branes: specific heat and DC conductivity. This behavior can be inferred from the dynamics of the fundamental strings which provide a good description of the probe branes in the regime of low temperatures and finite densities. We also comment on the speed of sound on the branes and the temperature dependence of DC conductivity at vanishing charge density.

We numerically investigate some properties of unbalanced St\"{u}ckelberg holographic superconductors, by considering backreaction effects of fields on the background geometry. More precisely, we study the impacts of the chemical potential mismatch and St\"{u}ckelberg mechanism on the condensation and conductivity types (electrical, spin, mixed, thermo-electric, thermo-spin and thermal conductivity). Our results show that the St\"{u}ckelberg's model parameters C_{alpha} and alpha not only have significant impacts on the phase transition, but also affect the conductivity pseudo-gap and the strength of conductivity fluctuations. Moreover, the effects of these parameters on a system will be gradually reduced as the imbalance grows. We also find that the influence of alpha on the amplitude of conductivity fluctuations depends on the magnitude of the both C_{alpha} and deltamu/mu in the electric and thermal conductivity cases. This results in that increasing alpha can damp the conductivity fluctuations of an unbalanced system in contrast to balanced ones.

We study several aspects of charged dilaton black holes with planar symmetry in (d+2)-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schr\"{o}dinger equation and find that the AC conductivity behaves like omega^{delta}, where the exponent delta is determined by the dilaton coupling alpha and the spacetime dimension parameter d. Moreover, we also study the Gauss-Bonnet corrections to eta/s in a five-dimensional finite-temperature background.

This article is about the neural conundrum behind the slowness of human behavior. The information throughput of a human being is about 10 bits/s. In comparison, our sensory systems gather data at ~10^9 bits/s. The stark contrast between these numbers remains unexplained and touches on fundamental aspects of brain function: What neural substrate sets this speed limit on the pace of our existence? Why does the brain need billions of neurons to process 10 bits/s? Why can we only think about one thing at a time? The brain seems to operate in two distinct modes: the "outer" brain handles fast high-dimensional sensory and motor signals, whereas the "inner" brain processes the reduced few bits needed to control behavior. Plausible explanations exist for the large neuron numbers in the outer brain, but not for the inner brain, and we propose new research directions to remedy this.

We construct holographic superconductors from Einstein-Maxwell-dilaton gravity in 3+1 dimensions with two adjustable couplings alpha and the charge q carried by the scalar field. For the values of alpha and q we consider, there is always a critical temperature at which a second order phase transition occurs between a hairy black hole and the AdS RN black hole in the canonical ensemble, which can be identified with the superconducting phase transition of the dual field theory. We calculate the electric conductivity of the dual superconductor and find that for the values of alpha and q where alpha/q is small the dual superconductor has similar properties to the minimal model, while for the values of alpha and q where alpha/q is large enough, the electric conductivity of the dual superconductor exhibits novel properties at low frequencies where it shows a "Drude Peak" in the real part of the conductivity.

We verify a recent prediction (Eq. 3.50 in G. L. Eyink, Phys. Rev. X 11, 031054 (2021)) for the drag on an object moving through a fluid. In this prediction the velocity field is decomposed into a nonvortical (potential) and vortical contribution, and so is the associated drag force. In the Josephson-Anderson relation the vortical contribution of the drag force follows from the flux of vorticity traversing the streamlines of the corresponding potential flow. The potential component is directly determined by the plate acceleration and its added mass. The Josephson-Anderson relation is derived from the quantum description of superfluids, but remarkably applies to the classical fluid in our experiment. In our experiment a flat plate is accelerated through water using a robotic arm. This geometry is simple enough to allow analytic potential flow streamlines. The monitored plate position shows an oscillatory component of the acceleration, which adds an additional test of the Josephson-Anderson relation. The instantaneous velocity field is measured using particle image velocimetry. It enables us to evaluate Eq. 3.50 from [1] and compare its prediction to the measured drag force. We find excellent agreement, and, most remarkably find that the added mass contribution to the drag force still stands out after the flow has turned vortical. We finally comment on the requirements on the experimental techniques for evaluating the Josephson-Anderson relation.

We study black branes carrying both electric and magnetic charges in Einstein-Maxwell theory coupled to a dilaton-axion in asymptotically anti de Sitter space. After reviewing and extending earlier results for the case of electrically charged branes, we characterise the thermodynamics of magnetically charged branes. We then focus on dyonic branes in theories which enjoy an SL(2,R) electric-magnetic duality. Using SL(2,R), we are able to generate solutions with arbitrary charges starting with the electrically charged solution, and also calculate transport coefficients. These solutions all exhibit a Lifshitz-like near-horizon geometry. The system behaves as expected for a charged fluid in a magnetic field, with non-vanishing Hall conductance and vanishing DC longitudinal conductivity at low temperatures. Its response is characterised by a cyclotron resonance at a frequency proportional to the magnetic field, for small magnetic fields. Interestingly, the DC Hall conductance is related to the attractor value of the axion. We also study the attractor flows of the dilaton-axion, both in cases with and without an additional modular-invariant scalar potential. The flows exhibit intricate behaviour related to the duality symmetry. Finally, we briefly discuss attractor flows in more general dilaton-axion theories which do not enjoy SL(2,R) symmetry.

We investigate properties of holographic strange metals in p+2-dimensions, generalizing the analysis performed in arXiv:0912.1061. The bulk spacetime is p+2-dimensional Lifshitz black hole, while the role of charge carriers is played by probe D-branes. We mainly focus on massless charge carriers, where most of the results can be obtained analytically. We obtain exact results for the free energy and calculate the entropy density, the heat capacity as well as the speed of sound at low temperature. We obtain the DC conductivity and DC Hall conductivity and find that the DC conductivity takes a universal form in the large density limit, while the Hall conductivity is also universal in all dimensions. We also study the resistivity in different limits and clarify the condition for the linear dependence on the temperature, which is a key feature of strange metals. We show that our results for the DC conductivity are consistent with those obtained via Kubo formula and we obtain the charge diffusion constant analytically. The corresponding properties of massive charge carriers are also discussed in brief.

We describe a new detector, called NuLat, to study electron anti-neutrinos a few meters from a nuclear reactor, and search for anomalous neutrino oscillations. Such oscillations could be caused by sterile neutrinos, and might explain the "Reactor Antineutrino Anomaly". NuLat, is made possible by a natural synergy between the miniTimeCube and mini-LENS programs described in this paper. It features a "Raghavan Optical Lattice" (ROL) consisting of 3375 boron or ^6Li loaded plastic scintillator cubical cells 6.3\,cm (2.500") on a side. Cell boundaries have a 0.127\,mm (0.005") air gap, resulting in total internal reflection guiding most of the light down the 3 cardinal directions. The ROL detector technology for NuLat gives excellent spatial and energy resolution and allows for in-depth event topology studies. These features allow us to discern inverse beta decay (IBD) signals and the putative oscillation pattern, even in the presence of other backgrounds. We discuss here test venues, efficiency, sensitivity and project status.

We consider holographic superconductors whose bulk description consists of gravity minimally coupled to a Maxwell field and charged scalar field with general potential. We give an analytic argument that there is no "hard gap": the real part of the conductivity at low frequency remains nonzero (although typically exponentially small) even at zero temperature. We also numerically construct the gravitational dual of the ground state of some holographic superconductors. Depending on the charge and dimension of the condensate, the infrared theory can have emergent conformal or just Poincare symmetry. In all cases studied, the area of the horizon of the dual black hole goes to zero in the extremal limit, consistent with a nondegenerate ground state.

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the DC ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero DC conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semi-circle transitions between them. The model can be regarded as a strongly coupled analog of the old `composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model.