# D. Feldman - Landau Institute for Theoretical Physics

## Contact Details

NameD. Feldman |
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AffiliationLandau Institute for Theoretical Physics |
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Location |
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## Pubs By Year |
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## External Links |
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## Pub CategoriesHigh Energy Physics - Phenomenology (21) Physics - Mesoscopic Systems and Quantum Hall Effect (15) High Energy Physics - Experiment (6) High Energy Astrophysical Phenomena (6) Physics - Strongly Correlated Electrons (6) Physics - Statistical Mechanics (4) Computer Science - Data Structures and Algorithms (3) Solar and Stellar Astrophysics (3) High Energy Physics - Theory (2) Physics - Superconductivity (2) Mathematics - Combinatorics (2) Computer Science - Learning (1) Mathematics - Number Theory (1) Mathematics - Metric Geometry (1) Cosmology and Nongalactic Astrophysics (1) Quantum Physics (1) Computer Science - Robotics (1) Astrophysics of Galaxies (1) Computer Science - Computer Vision and Pattern Recognition (1) Earth and Planetary Astrophysics (1) Physics - Accelerator Physics (1) Statistics - Machine Learning (1) Physics - Instrumentation and Detectors (1) |

## Publications Authored By D. Feldman

How can we train a statistical mixture model on a massive data set? In this paper, we show how to construct coresets for mixtures of Gaussians and natural generalizations. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being independent of the data set size. Read More

We present a library of empirical stellar spectra created using spectra from the Sloan Digital Sky Survey's Baryon Oscillation Spectroscopic Survey (BOSS). The templates cover spectral types O5 through L3, are binned by metallicity from -2.0 dex through +1. Read More

A fractional quasiparticle charge is a manifestation of strong interactions in the fractional quantum Hall effect. Nevertheless, shot noise of quasiparticles is well described by a formula, derived for noninteracting charges. We explain the success of that formula by proving that in the limits of strong and weak backscattering it holds irrespectively of microscopic details in weakly and strongly interacting systems alike. Read More

Let $P$ be a set (called points), $Q$ be a set (called queries) and a function $ f:P\times Q\to [0,\infty)$ (called cost). For an error parameter $\epsilon>0$, a set $S\subseteq P$ with a \emph{weight function} $w:P \rightarrow [0,\infty)$ is an $\epsilon$-coreset if $\sum_{s\in S}w(s) f(s,q)$ approximates $\sum_{p\in P} f(p,q)$ up to a multiplicative factor of $1\pm\epsilon$ for every given query $q\in Q$. We construct coresets for the $k$-means clustering of $n$ input points, both in an arbitrary metric space and $d$-dimensional Euclidean space. Read More

We investigate the thermoelectric current and heat conductance in a chiral Josephson contact on a surface of a 3D topological insulator, covered with superconducting and magnetic insulator films. The contact consists of two junctions of Majorana and Dirac channels next to two superconductors. Geometric asymmetry results in a supercurrent without a phase bias. Read More

The quantum of heat conductance of ballistic one-dimensional (1D) channels, being gQ=k0T with k0=pi^2*2kB^2/3h (T - temperature, kB - Boltzmann's constant, h - Planck's constant), is an important fundamental constant. While the quantization of the electrical conductance of 1D ballistic conductors has long been experimentally established, a demonstration of the quantization of thermal conductance proved to be much harder. It has already been accomplished for weakly interacting systems of phonons, photons, and electronic Fermi-liquids. Read More

**Authors:**Joseph E. Rodriguez, Keivan G. Stassun, Phillip Cargile, Benjamin J. Shappee, Robert J. Siverd, Joshua Pepper, Michael B. Lund, Christopher S. Kochanek, David James, Rudolf B. Kuhn, Thomas G. Beatty, B. Scott Gaudi, David A. Weintraub, Krzysztof Z. Stanek, Thomas W. S. Holoien, Jose L. Prieto, Daniel M. Feldman, Catherine C. Espaillat

**Category:**Solar and Stellar Astrophysics

In some planet formation theories, protoplanets grow gravitationally within a young star's protoplanetary disk, a signature of which may be a localized disturbance in the disk's radial and/or vertical structure. Using time-series photometric observations by the Kilodegree Extremely Little Telescope South (KELT-South) project and the All-Sky Automated Survey for SuperNovae (ASAS-SN), combined with archival observations, we present the discovery of two extended dimming events of the young star, DM Ori. This young system faded by $\sim$1. Read More

Numerical results suggest that the quantum Hall effect at {\nu} = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. Read More

We provide the first streaming algorithm for computing a provable approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes entries, and $d\geq n$. E. Read More

In the pose-estimation problem we need to align a set of $n$ markers (points in 3D space) and choose one of their n! permutations, so that the sum of squared corresponding distances to another ordered set of $n$ markers is minimized. We prove that every set has a weighted subset (core-set) of constant size (independent of $n$), such that computing the optimal orientation of the small core-set would yield exactly the same result as using the full set of $n$ markers. A deterministic algorithm for computing this core-set in $O(n)$ time is provided, using the Caratheodory Theorem from computational geometry. Read More

Because of the bulk gap, low energy physics in the quantum Hall effect is confined to the edges of the 2D electron liquid. The velocities of edge modes are key parameters of edge physics. They were determined in several quantum Hall systems from time-resolved measurements and high-frequency ac transport. Read More

Resolved submillimeter imaging of transitional disks is increasingly revealing the complexity of disk structure. Here we present the first high-resolution submillimeter image of a recently identified transitional disk around IRAS 04125+2902 in the Taurus star-forming region. We measure an inner disk hole of ~20 AU around IRAS 04125+2902 by simultaneously modeling new 880 micron Submillimeter Array (SMA) data along with an existing spectral energy distribution supplemented by new Discovery Channel Telescope (DCT) photometry. Read More

In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the low rank approximation (reduced SVD) of such matrices. Our solution uses coresets, which is a subset of $O(k/\eps^2)$ scaled rows from the $n\times d$ input matrix, that approximates the sub of squared distances from its rows to every $k$-dimensional subspace in $\REAL^d$, up to a factor of $1\pm\eps$. Read More

The fluctuation theorem establishes general relations between transport coefficients and fluctuations in nonequilibrium systems. Recently there was much interest in quantum fluctuation relations for electric currents. Since charge carriers also carry spin, it is important to extend the fluctuation theorem to spin currents. Read More

Several topological orders have been proposed to explain the quantum Hall plateau at $\nu=5/2$. The observation of an upstream neutral mode on the sample edge [Bid et al., Nature (London) 466, 585 (2010)] supports the non-Abelian anti-Pfaffian state. Read More

Fluctuation theorems establish deep relations between observables away from thermal equilibrium. Until recently, the research on fluctuation theorems was focused on time-reversal-invariant systems. In this review we address some newly discovered fluctuation relations that hold without time-reversal symmetry, in particular, in the presence of an external magnetic field. Read More

Majorana fermions often coexist with other low-energy fermionic degrees of freedom. In such situation, topological quantum computation requires the use of fermionic zero modes of a many-body system. We classify all such modes for interacting fermions and show how to select the mode that maximizes the decoherence time. Read More

**Authors:**Halina Abramowicz, Angel Abusleme, Konstatin Afanaciev, Gideon Alexander, Niloufar Alipour Tehrani, Oscar Alonso, Kristoffer K. Andersen, Samir Arfaoui, Csaba Balazs, Tim Barklow, Marco Battaglia, Mathieu Benoit, Burak Bilki, Jean-Jacques Blaising, Mark Boland, Marça Boronat, Ivanka Božović Jelisavčić, Philip Burrows, Maximilien Chefdeville, Roberto Contino, Dominik Dannheim, Marcel Demarteau, Marco Aurelio Diaz Gutierrez, Angel Diéguez, Jorge Duarte Campderros, Gerald Eigen, Konrad Elsener, Dan Feldman, Uli Felzmann, Mirosław Firlej, Elena Firu, Tomasz Fiutowski, Kurt Francis, Frank Gaede, Ignacio García García, Veta Ghenescu, Gian Giudice, Norman Graf, Christian Grefe, Christophe Grojean, Rick S. Gupta, Michael Hauschild, Helga Holmestad, Marek Idzik, Christian Joram, Sergey Kananov, Yannis Karyotakis, Martin Killenberg, Wolfgang Klempt, Sabine Kraml, Beata Krupa, Szymon Kulis, Tomáš Laštovička, Greg LeBlanc, Aharon Levy, Itamar Levy, Lucie Linssen, Angela Lucaci Timoce, Strahinja Lukić, Vladimir Makarenko, John Marshall, Victoria Martin, Rune E. Mikkelsen, Gordana Milutinović-Dumbelović, Akiya Miyamoto, Klaus Mönig, Gudrid Moortgat-Pick, Jakub Moroń, Astrid Münnich, Alina Neagu, Mila Pandurović, Duccio Pappadopulo, Bogdan Pawlik, Werner Porod, Stéphane Poss, Titi Preda, Roger Rassool, Ricardo Rattazzi, Sophie Redford, Jose Repond, Sabine Riemann, Aidan Robson, Philipp Roloff, Eduardo Ros, Jonatan Rosten, Alberto Ruiz-Jimeno, Heidi Rzehak, André Sailer, Dieter Schlatter, Daniel Schulte, Felix Sefkow, Katja Seidel, Nikolai Shumeiko, Eva Sicking, Frank Simon, Jacob Smith, Christian Soldner, Steinar Stapnes, Jan Strube, Taikan Suehara, Krzysztof Świentek, Marco Szalay, Tomohiko Tanabe, Michal Tesař, Andrea Thamm, Mark Thomson, Juan Trenado Garcia, Ulrik I. Uggerhøj, Erik van der Kraaij, Iván Vila, Eva Vilella, Miguel Angel Villarejo, Marcelo Alonso Vogel Gonzalez, Marcel Vos, Nigel Watson, Harry Weerts, James D. Wells, Lars Weuste, Tobias N. Wistisen, Kent Wootton, Lei Xia, Leszek Zawiejski, Ion-Sorin Zgura

This paper summarizes the physics potential of the CLIC high-energy e+e- linear collider. It provides input to the Snowmass 2013 process for the energy-frontier working groups on The Higgs Boson (HE1), Precision Study of Electroweak Interactions (HE2), Fully Understanding the Top Quark (HE3), as well as The Path Beyond the Standard Model -- New Particles, Forces, and Dimensions (HE4). It is accompanied by a paper describing the CLIC accelerator study, submitted to the Frontier Capabilities group of the Snowmass process. Read More

Two recent experiments [I. P. Radu et al. Read More

The breaking of electroweak symmetry through renormalization group flow in models that have MSSM spectra is found to produce "well-mixed" neutralino dark matter with a relic density consistent with the WMAP data and elastic scattering cross section with nuclei consistent with current limits from direct dark matter searches. These models predict a Higgs boson mass in the range (125-126) GeV. Well-mixed neutralino dark matter is predominantly bino-like, but has significant Higgsino and wino content, each with fractions of comparable size. Read More

Edges of some quantum Hall liquids and a number of other systems exhibit chiral transport: excitations can propagate in one direction only, e.g., clockwise. Read More

We present a study of an Hanbury Brown and Twiss (HBT) interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate HBT cross-correlations of Abelian Laughlin anyons. Read More

LHC-7 has narrowed down the mass range of the light Higgs boson. This result is consistent with the supergravity unification framework, and the current Higgs boson mass window implies a rather significant loop correction to the tree value pointing to a relatively heavy scalar sparticle spectrum with universal boundary conditions. It is shown that the largest value of the Higgs boson mass is obtained on the Hyperbolic Branch of radiative breaking. Read More

We investigate the connection between the conservation of R-parity in supersymmetry and the Stueckelberg mechanism for the mass generation of the B-L vector gauge boson. It is shown that with universal boundary conditions for soft terms of sfermions in each family at the high scale and with the Stueckelberg mechanism for generating mass for the B-L gauge boson present in the theory, electric charge conservation guarantees the conservation of R-parity in the minimal B-L extended supersymmetric standard model. We also discuss non-minimal extensions. Read More

The recent excess observed by CDF in $B^0_s \to \mu^{+} \mu^{-}$ is interpreted in terms of a possible supersymmetric origin. An analysis is given of the parameter space of mSUGRA and non-universal SUGRA models under the combined constraints from LHC-7 with 165 pb$^{-1}$ of integrated luminosity, under the new XENON-100 limits on the neutralino-proton spin independent cross section and under the CDF $B^0_s \to \mu^{+} \mu^{-}$ 90% C.L. Read More

Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to approximate a set $P$ of $n$ elements (say, points) by a shape $x$ from a (possibly infinite) family $X$ of shapes. Here, each point $p\in P$ corresponds to a function $f$ such that $f(x)$ is the distance from $p$ to $x$, and we seek a shape $x$ that minimizes the sum of distances from each point in $P$. Read More

We point out that in theories where the gravitino mass, $M_{3/2}$, is in the range (10-50)TeV, with soft-breaking scalar masses and trilinear couplings of the same order, there exists a robust region of parameter space where the conditions for electroweak symmetry breaking (EWSB) are satisfied without large imposed cancellations. Compactified string/M-theory with stabilized moduli that satisfy cosmological constraints generically require a gravitino mass greater than about 30 TeV and provide the natural explanation for this phenomenon. We find that even though scalar masses and trilinear couplings (and the soft-breaking $B$ parameter) are of order (10-50)TeV, the Higgs vev takes its expected value and the $\mu$ parameter is naturally of order a TeV. Read More

We consider a three-terminal system with a chiral edge channel connecting the source and drain terminals. Charge can tunnel between the chiral edge and a third terminal. The third terminal is maintained at a different temperature and voltage than the source and drain. Read More

Constraints on dark matter from the first CMS and ATLAS SUSY searches are investigated. It is shown that within the minimal supergravity model, the early search for supersymmetry at the LHC has depleted a large portion of the signature space in dark matter direct detection experiments. In particular, the prospects for detecting signals of dark matter in the XENON and CDMS experiments are significantly affected in the low neutralino mass region. Read More

The CMS and the ATLAS Collaborations have recently reported on the search for supersymmetry with 35 pb$^{-1}$ of data and have put independent limits on the parameter space of the supergravity unified model with universal boundary conditions at the GUT scale for soft breaking, i.e., the mSUGRA model. Read More

We present a focused study of a predictive unified model whose measurable consequences are immediately relevant to early discovery prospects of supersymmetry at the LHC. ATLAS and CMS have released their analysis with 35~pb$^{-1}$ of data and the model class we discuss is consistent with this data. It is shown that with an increase in luminosity the LSP dark matter mass and the gluino mass can be inferred from simple observables such as kinematic edges in leptonic channels and peak values in effective mass distributions. Read More

We analyze supergravity models that predict a low mass gluino within the landscape of sparticle mass hierarchies. The analysis includes a broad class of models that arise in minimal and in non-minimal supergravity unified frameworks and in extended models with additional $U(1)^n_X$ hidden sector gauge symmetries. Gluino masses in the range $(350-700)$ GeV are investigated. Read More

A solution to the PAMELA positron excess with Higgsino dark matter within extended supergravity grand unified (SUGRA) models is proposed. The models are compliant with the photon constraints recently set by Fermi-LAT and produce positron as well as antiproton fluxes consistent with the PAMELA experiment. The SUGRA models considered have an extended hidden sector with extra degrees of freedom which allow for a satisfaction of relic density consistent with WMAP. Read More

We investigate rectification of a low-frequency ac bias in Y-junctions of one-channel Luttinger liquid wires with repulsive electron interaction. Rectification emerges due to three scatterers in the wires. We find that it is possible to achieve a higher rectification current in a Y-junction than in a single wire with an asymmetric scatterer at the same interaction strength and voltage bias. Read More

It has been shown recently that non-Abelian states and the spin-polarized and unpolarized versions of the Abelian 331 state may have identical signatures in Fabry-P\'{e}rot interferometry in the quantum Hall effect at filling factor 5/2. We calculate the Fano factor for the shot noise in a Mach-Zehnder interferometer in the 331 states and demonstrate that it differs from the Fano factor in the proposed non-Abelian states. The Fano factor depends periodically on the magnetic flux through the interferometer. Read More

Our earlier article proved that if $n > 1$ translates of sublattices of $Z^d$ tile $Z^d$, and all the sublattices are Cartesian products of arithmetic progressions, then two of the tiles must be translates of each other. We re-prove this Theorem, this time using generating functions. We also show that for $d \geq 1$, not every finite tiling of $Z^d$ by lattices can be obtained from the trivial tiling by the process of repeatedly subdividing a tile into sub-tiles that are translates of one another. Read More

Most analyses of dark matter within supersymmetry assume the entire cold dark matter arising only from weakly interacting neutralinos. We study a new class of models consisting of $U(1)^n$ hidden sector extensions of the MSSM that includes several stable particles, both fermionic and bosonic, which can be interpreted as constituents of dark matter. In one such class of models, dark matter is made up of both a Majorana dark matter particle, i. Read More

The region of low neutralino masses as low as (5-10) GeV has attracted attention recently due to the possibility of excess events above background in dark matter detectors. An analysis of spin independent neutralino-proton cross sections $\SI$ which includes this low mass region is given. The analysis is done in MSSM with radiative electroweak symmetry breaking (REWSB). Read More

Motivated by specific connections to dark matter signatures, we study the prospects of observing the presence of a relatively light gluino whose mass is in the range ~(500-900) GeV with a wino-like lightest supersymmetric particle with mass in the range of ~(170-210) GeV. The light gaugino spectra studied here is generally different from other models, and in particular those with a wino dominated LSP, in that here the gluinos can be significantly lighter. The positron excess reported by the PAMELA satellite data is accounted for by annihilations of the wino LSP and their relic abundance can generally be brought near the WMAP constraints due to the late decay of a modulus field re-populating the density of relic dark matter. Read More

**Authors:**P. Nath, B. D. Nelson, H. Davoudiasl, B. Dutta, D. Feldman, Z. Liu, T. Han, P. Langacker, R. Mohapatra, J. Valle, A. Pilaftsis, D. Zerwas, S. AbdusSalam, C. Adam-Bourdarios, J. A. Aguilar-Saavedra, B. Allanach, B. Altunkaynak, L. A. Anchordoqui, H. Baer, B. Bajc, O. Buchmueller, M. Carena, R. Cavanaugh, S. Chang, K. Choi, C. Csaki, S. Dawson, F. de Campos, A. De Roeck, M. Duhrssen, O. J. P. Eboli, J. R. Ellis, H. Flacher, H. Goldberg, W. Grimus, U. Haisch, S. Heinemeyer, M. Hirsch, M. Holmes, T. Ibrahim, G. Isidori, G. Kane, K. Kong, R. Lafaye, G. Landsberg, L. Lavoura, J. S. Lee, S. J. Lee, M. Lisanti, D. Lust, M. B. Magro, R. Mahbubani, M. Malinsky, F. Maltoni, S. Morisi, M. M. Muhlleitner, B. Mukhopadhyaya, M. Neubert, K. A. Olive, G. Perez, P. Fileviez Perez, T. Plehn, E. Ponton, W. Porod, F. Quevedo, M. Rauch, D. Restrepo, T. G. Rizzo, J. C. Romao, F. J. Ronga, J. Santiago, J. Schechter, G. Senjanovic, J. Shao, M. Spira, S. Stieberger, Z. Sullivan, T. M. P. Tait, X. Tata, T. R. Taylor, M. Toharia, J. Wacker, C. E. M. Wagner, L. -T. Wang, G. Weiglein, D. Zeppenfeld, K. Zurek

**Category:**High Energy Physics - Phenomenology

The Large Hadron Collider presents an unprecedented opportunity to probe the realm of new physics in the TeV region and shed light on some of the core unresolved issues of particle physics. These include the nature of electroweak symmetry breaking, the origin of mass, the possible constituent of cold dark matter, new sources of CP violation needed to explain the baryon excess in the universe, the possible existence of extra gauge groups and extra matter, and importantly the path Nature chooses to resolve the hierarchy problem - is it supersymmetry or extra dimensions. Many models of new physics beyond the standard model contain a hidden sector which can be probed at the LHC. Read More

An analysis is given connecting event rates for the direct detection of neutralino dark matter with the possible signatures of supersymmetry at the LHC. It is shown that if an effect is seen in the direct detection experiments at a level of $O(10^{-44})$ cm$^2$ for the neutralino-proton cross section, then within the mSUGRA model the next heavier particle above the neutralino is either a stau, a chargino, or a CP odd/CP even (A/H) Higgs boson. Further, the collider analysis shows that models with a neutralino-proton cross section at the level of $(1-5)\times 10^{-44}$ cm$^2$ could be probed with as little as 1 fb$^{-1}$ of integrated luminosity at the LHC at $\sqrt s=10$ TeV. Read More

Recent re-evaluations of the Standard Model (SM) contribution to ${\mathcal Br(b\to s\gamma)$ hint at a positive correction from new physics. Since a charged Higgs boson exchange always gives a positive contribution to this branching ratio, the constraint points to the possibility of a relatively light charged Higgs. It is found that under the HFAG constraints and with re-evaluated SM results large cancellations between the charged Higgs and the chargino contributions in supersymmetric models occur. Read More

We calculate the tunneling current through long line junctions of a $\nu=5/2$ quantum Hall liquid and i) another $\nu=5/2$ liquid, ii) an integer quantum Hall liquid and iii) a quantum wire. Momentum resolved tunneling provides information about the number, propagation directions and other features of the edge modes and thus helps distinguish several competing models of the 5/2 state. We investigate transport properties of two proposed Abelian states: $K=8 state and 331 state, and four possible non-Abelian states: Pfaffian, edge-reconstructed Pfaffian, and two versions of the anti-Pfaffian state. Read More

Signatures of soft supersymmetry breaking at the CERN LHC and in dark matter experiments are discussed with focus drawn to light superparticles, and in particular light gauginos and their discovery prospects. Connected to the above is the recent PAMELA positron anomaly and its implications for signatures of SUSY in early runs at the Large Hadron Collider. Other new possibilities for physics beyond the Standard Model are also briefly discussed. Read More

The PAMELA positron excess is analyzed within the framework of nonuniversal SUGRA models with an extended $U(1)^n$ gauge symmetry in the hidden sector leading to neutralino dark matter with either a mixed Higgsino-wino LSP or an essentially pure wino dominated LSP. The Higgsino-wino LSP can produce the observed PAMELA positron excess and satisfy relic density constraints in the extended class of models due to a near degeneracy of the mass spectrum of the extended neutralino sector with the LSP mass. The simultaneous satisfaction of the WMAP relic density data and the PAMELA data is accomplished through a co-annihilation mechanism ($B_{\rm Co}-mechanism$), and leads to predictions of a neutralino and a chargino in the mass range (180-200) GeV as well as low lying sparticles accessible at colliders. Read More

The possibility that the gluino is the next to the lightest supersymmetric particle (NLSP) is discussed and it is shown that this situation arises in nonuniversal SUGRA models within a significant part of the parameter space compatible with all known experimental bounds. It is then shown that the gluino NLSP (GNLSP) models lead to a compressed sfermion spectrum with the sleptons often heavier than the squarks at least for the first two generations. The relic density here is governed by gluino coannihilation which is responsible for a relatively small mass splitting between the gluino and the neutralino masses. Read More

We use Fourier methods to prove that if $n > 1$ translates of sublattices of $Z^d$ tile $Z^d$, and all the sublattices are Cartesian products of arithmetic progressions, then two of the tiles must be translates of each other. This is a multi-dimensional generalization of the Mirsky-Newman Theorem. Read More

The recent positron excess observed in the PAMELA satellite experiment strengthens previous experimental findings. We give here an analysis of this excess in the framework of the Stueckelberg extension of the standard model which includes an extra $U(1)_X$ gauge field and matter in the hidden sector. Such matter can produce the right amount of dark matter consistent with the WMAP constraints. Read More

Theorem 1 Let F:N-->R stand for any function which a) $F$ monotonically weakly increases; b) $F$ tends to infinity; and c) such that $q/F(q)$ tends to infinity. Let Z_F(q) equal the number of divisors of q less than sqrt{F(q)} minus the number of divisors of q between sqrt{F(q)} and F(q). Then, on the average, Z_F(q) equals Euler's constant Theorem 2 Fix a in (0,1). Read More

**Category:**Mathematics - Metric Geometry

We use a probabilistic interpretation of solid angles to generalize the well-known fact that the inner angles of a triangle sum to 180 degrees. For the 3-dimensional case, we show that the sum of the solid inner vertex angles of a tetrahedron T, divided by 2*pi, gives the probability that an orthogonal projection of T onto a random 2-plane is a triangle. More generally, it is shown that the sum of the (solid) inner vertex angles of an n-simplex S, normalized by the area of the unit (n-1)-hemisphere, gives the probability that an orthogonal projection of S onto a random hyperplane is an (n-1)-simplex. Read More