Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations

In this work we investigate the sphaleron solution in a $SU(2)\times U(1)_X$ gauge theory, which also encompasses the Standard Model, with higher scalar representation(s) ($J^{(i)},X^{(i)}$). We show that the field profiles describing the sphaleron in higher scalar multiplet, have similar trends like the doublet case with respect to the radial distance. We compute the sphaleron energy and find that it scales linearly with the vacuum expectation value of the scalar field and its slope depends on the representation. We also investigate the effect of $U(1)$ gauge field and find that it is small for the physical value of the mixing angle, $\theta_{W}$ and resembles the case for the doublet. For higher representations, we show that the criterion for strong first order phase transition, $v_{c}/T_{c}>\eta$, is relaxed with respect to the doublet case, i.e. $\eta<1$.Comment: 20 pages, 5 figures & 1 table, published versio

Supergoop Dynamics

We initiate a systematic study of the dynamics of multi-particle systems with supersymmetric Van der Waals and electron-monopole type interactions. The static interaction allows a complex continuum of ground state configurations, while the Lorentz interaction tends to counteract this configurational fluidity by magnetic trapping, thus producing an exotic low temperature phase of matter aptly named supergoop. Such systems arise naturally in $\mathcal{N}=2$ gauge theories as monopole-dyon mixtures, and in string theory as collections of particles or black holes obtained by wrapping D-branes on internal space cycles. After discussing the general system and its relation to quiver quantum mechanics, we focus on the case of three particles. We give an exhaustive enumeration of the classical and quantum ground states of a probe in an arbitrary background with two fixed centers. We uncover a hidden conserved charge and show that the dynamics of the probe is classically integrable. In contrast, the dynamics of one heavy and two light particles moving on a line shows a nontrivial transition to chaos, which we exhibit by studying the Poincar\'e sections. Finally we explore the complex dynamics of a probe particle in a background with a large number of centers, observing hints of ergodicity breaking. We conclude by discussing possible implications in a holographic context.Comment: 35 pages,11 figures. v2: updated references to include a previous proof of classical integrability, exchanged a figure for a prettier versio

Explaining the t tbar forward-backward asymmetry without dijet or flavor anomalies

We consider new physics explanations of the anomaly in the top quark forward-backward asymmetry measured at the Tevatron, in the context of flavor conserving models. The recently measured LHC dijet distributions strongly constrain many otherwise viable models. A new scalar particle in the antitriplet representation of flavor and color can fit the t tbar asymmetry and cross section data at the Tevatron and avoid both low- and high-energy bounds from flavor physics and the LHC. An s-channel resonance in uc to uc scattering at the LHC is predicted to be not far from the current sensitivity. This model also predicts rich top quark physics for the early LHC from decays of the new scalar particles. Single production gives t tbar j signatures with high transverse momentum jet, pair production leads to t tbar j j and 4 jet final states.Comment: 7 pages, 6 figures; v2: notation clarified, references adde

Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions II - The deconfined phase

We present a non-perturbative study of the equation of state in the deconfined phase of Yang-Mills theories in D=2+1 dimensions. We introduce a holographic model, based on the improved holographic QCD model, from which we derive a non-trivial relation between the order of the deconfinement phase transition and the behavior of the trace of the energy-momentum tensor as a function of the temperature T. We compare the theoretical predictions of this holographic model with a new set of high-precision numerical results from lattice simulations of SU(N) theories with N=2, 3, 4, 5 and 6 colors. The latter reveal that, similarly to the D=3+1 case, the bulk equilibrium thermodynamic quantities (pressure, trace of the energy-momentum tensor, energy density and entropy density) exhibit nearly perfect proportionality to the number of gluons, and can be successfully compared with the holographic predictions in a broad range of temperatures. Finally, we also show that, again similarly to the D=3+1 case, the trace of the energy-momentum tensor appears to be proportional to T^2 in a wide temperature range, starting from approximately 1.2 T_c, where T_c denotes the critical deconfinement temperature.Comment: 2+36 pages, 10 figures; v2: comments added, curves showing the holographic predictions included in the plots of the pressure and energy and entropy densities, typos corrected: version published in JHE

Characterization of a Clp Protease Gene Regulator and the Reaeration Response in Mycobacterium tuberculosis

Mycobacterium tuberculosis (MTB) enters a non-replicating state when exposed to low oxygen tension, a condition the bacillus encounters in granulomas during infection. Determining how mycobacteria enter and maintain this state is a major focus of research. However, from a public health standpoint the importance of latent TB is its ability to reactivate. The mechanism by which mycobacteria return to a replicating state upon re-exposure to favorable conditions is not understood. In this study, we utilized reaeration from a defined hypoxia model to characterize the adaptive response of MTB following a return to favorable growth conditions. Global transcriptional analysis identified the ∼100 gene Reaeration Response, induced relative to both log-phase and hypoxic MTB. This response includes chaperones and proteases, as well as the transcription factor Rv2745c, which we characterize as a Clp protease gene regulator (ClgR) orthologue. During reaeration, genes repressed during hypoxia are also upregulated in a wave of transcription that includes genes crucial to transcription, translation and oxidative phosphorylation and culminates in bacterial replication. In sum, this study defines a new transcriptional response of MTB with potential relevance to disease, and implicates ClgR as a regulator involved in resumption of replication following hypoxia

Blood-Brain Barrier Permeability of Normal Appearing White Matter in Relapsing-Remitting Multiple Sclerosis

BACKGROUND: Multiple sclerosis (MS) affects the integrity of the blood-brain barrier (BBB). Contrast-enhanced T1 weighted magnetic resonance imaging (MRI) is widely used to characterize location and extent of BBB disruptions in focal MS lesions. We employed quantitative T1 measurements before and after the intravenous injection of a paramagnetic contrast agent to assess BBB permeability in the normal appearing white matter (NAWM) in patients with relapsing-remitting MS (RR-MS). METHODOLOGY/PRINCIPAL FINDINGS: Fifty-nine patients (38 females) with RR-MS undergoing immunomodulatory treatment and nine healthy controls (4 females) underwent quantitative T1 measurements at 3 tesla before and after injection of a paramagnetic contrast agent (0.2 mmol/kg Gd-DTPA). Mean T1 values were calculated for NAWM in patients and total cerebral white matter in healthy subjects for the T1 measurements before and after injection of Gd-DTPA. The pre-injection baseline T1 of NAWM (945±55 [SD] ms) was prolonged in RR-MS relative to healthy controls (903±23 ms, p = 0.028). Gd-DTPA injection shortened T1 to a similar extent in both groups. Mean T1 of NAWM was 866±47 ms in the NAWM of RR-MS patients and 824±13 ms in the white matter of healthy controls. The regional variability of T1 values expressed as the coefficient of variation (CV) was comparable between the two groups at baseline, but not after injection of the contrast agent. After intravenous Gd-DTPA injection, T1 values in NAWM were more variable in RR-MS patients (CV = 0.198±0.046) compared to cerebral white matter of healthy controls (CV = 0.166±0.018, p = 0.046). CONCLUSIONS/SIGNIFICANCE: We found no evidence of a global BBB disruption within the NAWM of RR-MS patients undergoing immunomodulatory treatment. However, the increased variation of T1 values in NAWM after intravenous Gd-DTPA injection points to an increased regional inhomogeneity of BBB function in NAWM in relapsing-remitting MS

Teaching energy conservation as a unifying principle in physics

In this work we present the design and assessment of a teaching sequence aimed at introducing the principle of energy conservation at post-compulsory secondary school level (16-18 year olds). The proposal is based on the result of research into teaching-learning difficulties and on the analysis of the physics framework. Evidence is shown that this teaching sequence, together with the methodology used in the classroom, may result in students having a better grasp of the principle of energy conservation. Keywords Physics education · Energy conceptions · Teaching activitie