Celebrating Cercignani's conjecture for the Boltzmann equation

Cercignani's conjecture assumes a linear inequality between the entropy and entropy production functionals for Boltzmann's nonlinear integral operator in rarefied gas dynamics. Related to the field of logarithmic Sobolev inequalities and spectral gap inequalities, this issue has been at the core of the renewal of the mathematical theory of convergence to thermodynamical equilibrium for rarefied gases over the past decade. In this review paper, we survey the various positive and negative results which were obtained since the conjecture was proposed in the 1980s.Comment: This paper is dedicated to the memory of the late Carlo Cercignani, powerful mind and great scientist, one of the founders of the modern theory of the Boltzmann equation. 24 pages. V2: correction of some typos and one ref. adde

Raised Intracellular Calcium Contributes to Ischemia-Induced Depression of Evoked Synaptic Transmission

Oxygen-glucose deprivation (OGD) leads to depression of evoked synaptic transmission, for which the mechanisms remain unclear. We hypothesized that increased presynaptic [Ca2+]i during transient OGD contributes to the depression of evoked field excitatory postsynaptic potentials (fEPSPs). Additionally, we hypothesized that increased buffering of intracellular calcium would shorten electrophysiological recovery after transient ischemia. Mouse hippocampal slices were exposed to 2 to 8 min of OGD. fEPSPs evoked by Schaffer collateral stimulation were recorded in the stratum radiatum, and whole cell current or voltage clamp recordings were performed in CA1 neurons. Transient ischemia led to increased presynaptic [Ca2+]i, (shown by calcium imaging), increased spontaneous miniature EPSP/Cs, and depressed evoked fEPSPs, partially mediated by adenosine. Buffering of intracellular Ca2+ during OGD by membrane-permeant chelators (BAPTA-AM or EGTA-AM) partially prevented fEPSP depression and promoted faster electrophysiological recovery when the OGD challenge was stopped. The blocker of BK channels, charybdotoxin (ChTX), also prevented fEPSP depression, but did not accelerate post-ischemic recovery. These results suggest that OGD leads to elevated presynaptic [Ca2+]i, which reduces evoked transmitter release; this effect can be reversed by increased intracellular Ca2+ buffering which also speeds recovery

Diversity amongst human cortical pyramidal neurons revealed via their sag currents and frequency preferences

In the human neocortex coherent interlaminar theta oscillations are driven by deep cortical layers, suggesting neurons in these layers exhibit distinct electrophysiological properties. To characterize this potential distinctiveness, we use in vitro whole-cell recordings from cortical layers 2 and 3 (L2&3), layer 3c (L3c) and layer 5 (L5) of the human cortex. Across all layers we observe notable heterogeneity, indicating human cortical pyramidal neurons are an electrophysiologically diverse population. L5 pyramidal cells are the most excitable of these neurons and exhibit the most prominent sag current (abolished by blockade of the hyperpolarization activated cation current, Ih). While subthreshold resonance is more common in L3c and L5, we rarely observe this resonance at frequencies greater than 2 Hz. However, the frequency dependent gain of L5 neurons reveals they are most adept at tracking both delta and theta frequency inputs, a unique feature that may indirectly be important for the generation of cortical theta oscillations

Optimal Hypercontractivity for Fermi Fields and Related Non-Commutative Integration

Optimal hypercontractivity bounds for the fermion oscillator semigroup are obtained. These are the fermion analogs of the optimal hypercontractivity bounds for the boson oscillator semigroup obtained by Nelson. In the process, several results of independent interest in the theory of non-commutative integration are established. {}.Comment: 18 p., princeton/ecel/7-12-9

Comment on "Why quantum mechanics cannot be formulated as a Markov process"

In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607, (1994)] claims that the theory of Markov stochastic processes cannot provide an adequate mathematical framework for quantum mechanics. In conjunction with the specific quantum dynamics considered there, we give a general analysis of the associated dichotomic jump processes. If we assume that Gillespie's "measurement probabilities" \it are \rm the transition probabilities of a stochastic process, then the process must have an invariant (time independent) probability measure. Alternatively, if we demand the probability measure of the process to follow the quantally implemented (via the Born statistical postulate) evolution, then we arrive at the jump process which \it can \rm be interpreted as a Markov process if restricted to a suitable duration time. However, there is no corresponding Markov process consistent with the $Z_2$ event space assumption, if we require its existence for all times $t\in R_+$.Comment: Latex file, resubm. to Phys. Rev.

On Visible Homelessness and the Micro-Aesthetics of Public Space

In this article, we investigate the circumstances that have produced the current municipal regulatory approach to homelessness in the City of Melbourne, Victoria, and the ways in which visibly homeless people are policed through a micro-aesthetics of their presence in public space, which involves the monitoring of their bodily demeanour and their physical possessions. Our study contributes to and draws from a range of debates, including studies of the governmental conjunction of poverty and crime, analysis of the co-implication of law and spatiality, research on the criminalisation of homelessness and homeless people, and the burgeoning criminological interest in the significance of the visual field for our understandings of crime and criminality. This article recounts how homelessness, public space and questions of aesthetics have recently coalesced in debates about the regulation of homelessness in the public space of Melbourne’s city centre. It approaches the issues through comparative consideration of genres of municipal management frameworks in other jurisdictions, detailed textual consideration of the Protocol on Homelessness in the City of Melbourne and an empirical study of visible homelessness in the public places of central Melbourne

'Prove me the bam!': victimization and agency in the lives of young women who commit violent offences

This article reviews the evidence regarding young women’s involvement in violent crime and, drawing on recent research carried out in HMPYOI Cornton Vale in Scotland, provides an overview of the characteristics, needs and deeds of young women sentenced to imprisonment for violent offending. Through the use of direct quotations, the article suggests that young women’s anger and aggression is often related to their experiences of family violence and abuse, and the acquisition of a negative worldview in which other people are considered as being 'out to get you' or ready to 'put one over on you'. The young women survived in these circumstances, not by adopting discourses that cast them as exploited victims, but by drawing on (sub)cultural norms and values which promote pre-emptive violence and the defence of respect. The implications of these findings for those who work with such young women are also discussed

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions $d\geq 2$ and in all of space for $d\geq 3$, the uniqueness being a result previously not known for PKS with degenerate diffusion. We generalize the notion of criticality for PKS and show that subcritical problems are globally well-posed. For a fairly general class of problems, we prove the existence of a critical mass which sharply divides the possibility of finite time blow up and global existence. Moreover, we compute the critical mass for fully general problems and show that solutions with smaller mass exists globally. For a class of supercritical problems we prove finite time blow up is possible for initial data of arbitrary mass.Comment: 31 page

The McKean-Vlasov Equation in Finite Volume

We study the McKean--Vlasov equation on the finite tori of length scale $L$ in $d$--dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are based on the criteria first uncovered in \cite{GP} and \cite{KM}. Therein and in subsequent works, one finds indications pointing to critical transitions at a particular model dependent value, $\theta^{\sharp}$ of the interaction parameter. We show that the uniform density (which may be interpreted as the liquid phase) is dynamically stable for $\theta < \theta^{\sharp}$ and prove, abstractly, that a {\it critical} transition must occur at $\theta = \theta^{\sharp}$. However for this system we show that under generic conditions -- $L$ large, $d \geq 2$ and isotropic interactions -- the phase transition is in fact discontinuous and occurs at some \theta\t < \theta^{\sharp}. Finally, for H--stable, bounded interactions with discontinuous transitions we show that, with suitable scaling, the \theta\t(L) tend to a definitive non--trivial limit as $L\to\infty$