The relationship between Heyting algebras (HA) and semirings is explored. A new class of HAs called Symmetric Heyting algebras (SHAs) is proposed, and a necessary condition on SHAs to be consider semirings is given. We define a new mathematical famil
y called Heyting structures, which are similar to semirings, but with Heyting-algebra operators in place of the usual arithmetic operators usually seen in semirings. The impact of the zero-sum free property of semirings on Heyting structures is shown as also the condition under which it is possible to extend one Heyting structure to another. It is also shown that the union of two or more sets forming Heyting structures is again a Heyting structure, if the operators on the new structure are suitably derived from those of the component structures. The analysis also provides a sufficient condition such that the larger Heyting structure satisfying a monotony law implies that the ones forming the union do so as well.
In 1994, Talagrand showed a generalization of the celebrated KKL theorem. In this work, we prove that the converse of this generalization also holds. Namely, for any sequence of numbers $0<a_1,a_2,ldots,a_nle 1$ such that $sum_{j=1}^n a_j/(1-log a_j)
ge C$ for some constant $C>0$, it is possible to find a roughly balanced Boolean function $f$ such that $textrm{Inf}_j[f] < a_j$ for every $1 le j le n$.
Context: In April 2013, the nearby (z=0.031) TeV blazar, Mkn 421, showed one of the largest flares in X-rays since the past decade. Aim: To study all multiwavelength data available during MJD 56392 to 56403, with special emphasis on X-ray data, and u
nderstand the underlying particle energy distribution. Methods: We study the correlations between the UV and gamma bands with the X-ray band using the z-transformed discrete correlation function. We model the underlying particle spectrum with a single population of electrons emitting synchrotron radiation, and do a statistical fitting of the simultaneous, time-resolved data from the Swift-XRT and the NuSTAR. Results: There was rapid flux variability in the X-ray band, with a minimum doubling timescale of $1.69 pm 0.13$ hrs. There were no corresponding flares in UV and gamma bands. The variability in UV and gamma rays are relatively modest with $ sim 8 % $ and $sim 16 % $ respectively, and no significant correlation was found with the X-ray light curve. The observed X-ray spectrum shows clear curvature which can be fit by a log parabolic spectral form. This is best explained to originate from a log parabolic electron spectrum. However, a broken power law or a power law with an exponentially falling electron distribution cannot be ruled out either. Moreover, the excellent broadband spectrum from $0.3-79$ keV allows us to make predictions of the UV flux. We find that this prediction is compatible with the observed flux during the low state in X-rays. However, during the X-ray flares, the predicted flux is a factor of $2-50$ smaller than the observed one. This suggests that the X-ray flares are plausibly caused by a separate population which does not contribute significantly to the radiation at lower energies. Alternatively, the underlying particle spectrum can be much more complex than the ones explored in this work.
At NISER-IoP detector laboratory an initiative is taken to build and test Gas Electron Multiplier (GEM) detectors for ALICE experiment. The optimisation of the gas flow rate and the long-term stability test of the GEM detector are performed. The method and test results are presented.
We study a class of nonequilibrium lattice models on a ring where particles hop in a particular direction, from a site to one of its (say, right) nearest neighbours, with a rate that depends on the occupation of all the neighbouring sites within a ra
nge R. This finite range process (FRP) for R=0 reduces to the well known zero-range process (ZRP), giving rise to a factorized steady state (FSS) for any arbitrary hop rate. We show that, provided the hop rates satisfy a specific condition, the steady state of FRP can be written as a product of cluster-weight function of (R+1) occupation variables. We show that, for a large class of cluster-weight functions, the cluster-factorized steady state admits a finite dimensional transfer-matrix formulation, which helps in calculating the spatial correlation functions and subsystem mass distributions exactly. We also discuss a criterion for which the FRP undergoes a condensation transition.
We analyze the quantum melting of two-dimensional Wigner molecules (WM) in confined geometries with distinct symmetries and compare it with corresponding thermal melting. Our findings unfold complementary mechanisms that drive the quantum and thermal
crossovers in a WM and show that the symmetry of the confinement plays no significant role in determining the quantum crossover scale $n_X$. This is because the zero-point motion screens the boundary effects within short distances. The phase diagram as a function of thermal and quantum fluctuations determined from independent criteria is unique, and shows melting from the WM to both the classical and quantum liquids. An intriguing signature of weakening liquidity with increasing temperature, $T$, is found in the extreme quantum regime. The crossover is associated with production of defects. However, these defects appear to play distinct roles in driving the quantum and thermal melting. Our study will help comprehending melting in a variety of experimental traps - from quantum dots to complex plasma.
The dynamical response of Coulomb-interacting particles in nano-clusters are analyzed at different temperatures characterizing their solid- and liquid-like behavior. Depending on the trap-symmetry, both the spatial and temporal correlations undergo s
low, stretched exponential relaxations at long times, arising from spatially correlated motion in string-like paths. Our results indicate that the distinction between the `solid and `liquid is soft: While particles in a `solid flow producing dynamic heterogeneities, motion in `liquid yields unusually long tail in the distribution of particle-displacements. A phenomenological model captures much of the subtleties of our numerical simulations.
A dataset has been classified by some unknown classifier into two types of points. What were the most important factors in determining the classification outcome? In this work, we employ an axiomatic approach in order to uniquely characterize an infl
uence measure: a function that, given a set of classified points, outputs a value for each feature corresponding to its influence in determining the classification outcome. We show that our influence measure takes on an intuitive form when the unknown classifier is linear. Finally, we employ our influence measure in order to analyze the effects of user profiling on Googles online display advertising.
We study solar cell properties of single silicon wires connected at their ends to two dissimilar metals of different work functions. Effects of wire dimensions, the work functions of the metals, and minority carrier lifetimes on short circuit current
as well as open circuit voltage are studied. The most efficient photovoltaic behavior is found to occur when one metal makes a Schottky contact with the wire, and the other makes an Ohmic contact. As wire length increases, both short circuit current and open circuit voltage increase before saturation occurs. Depending on the work function difference between the metals and the wire dimensions, the saturation length increases by approximately an order of magnitude with a two order magnitude increase in minority carrier length. However current per surface area exposed to light is found to decrease rapidly with increase in length. The use of a multi-contact interdigitated design for long wires is investigated to increase the photovoltaic response of the devices.
Higgs signatures from the cascade decays of light stops are an interesting possibility in the next to minimal supersymmetric standard model (NMSSM). We investigate the potential reach of the light stop mass at the 13 TeV run of the LHC by means of fi
ve NMSSM benchmark points where this signature is dominant. These benchmark points are compatible with current Higgs coupling measurements, LHC constraints, dark matter relic density and direct detection constraints. We consider single and di-lepton search strategies, as well as the jet-substructure technique to reconstruct the Higgs bosons. We find that one can probe stop masses up to 1.2 TeV with 300 $rm fb^{-1}$ luminosity via the di-lepton channel, while with the jet-substructure method, stop masses up to 1 TeV can be probed with 300 $rm fb^{-1}$ luminosity. We also investigate the possibility of the appearance of multiple Higgs peaks over the background in the fat-jet mass distribution, and conclude that such a possibility is viable only at the high luminosity run of 13 TeV LHC.
