Gas-solid coexistence of adhesive spheres

In this note, the authors investigate whether the gas-liquid critical point can remain stable with respect to solidification for narrow attractive interactions down to the Baxter limit. Using a crude cell theory, the authors estimate the necessary conditions for this to be true. Possible realizations are briefly discussed.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.

Fermion Mass Generation without Spontaneous Symmetry Breaking

The conventional mechanism of fermion mass generation in the Standard Model involves Spontaneous Symmetry Breaking (SSB). In this thesis, we study an alternate mechanism for the generation of fermion masses that does not require SSB, in the context of lattice field theories. Being inherently strongly coupled, this mechanism requires a non-perturbative approach like the lattice approach.

In order to explore this mechanism, we study a simple lattice model with a four-fermion interaction that has massless fermions at weak couplings and massive fermions at strong couplings, but without any spontaneous symmetry breaking. Prior work on this type of mass generation mechanism in 4D, was done long ago using either mean-field theory or Monte-Carlo calculations on small lattices. In this thesis, we have developed a new computational approach that enables us to perform large scale quantum Monte-Carlo calculations to study the phase structure of this theory. In 4D, our results confirm prior results, but differ in some quantitative details of the phase diagram. In contrast, in 3D, we discover a new second order critical point using calculations on lattices up to size $ 60^3$. Such large scale calculations are unprecedented. The presence of the critical point implies the existence of an alternate mechanism of fermion mass generation without any SSB, that could be of interest in continuum quantum field theory.

On the Origin of Natural Antibody

Natural IgM (nIgM) is constitutively present in the serum, where it aids in the early control of viral and bacterial expansions. nIgM also plays a significant role in the prevention of autoimmune disease by promoting the clearance of cellular debris. However, the cells that maintain high titers of nIgM in the circulation had not yet been identified. Several studies have linked serum nIgM with the presence of fetal-lineage B cells, and others have detected IgM secretion directly by B1a cells in various tissues. Nevertheless, a substantial contribution of undifferentiated B1 cells to nIgM titers is doubtful, as the ability to produce large quantities of antibody (Ab) is a function of the phenotype and morphology of differentiated plasma cells (PCs). No direct evidence exists to support the claim that a B1-cell population directly produces the bulk of circulating nIgM. The source of nIgM thus remained uncertain and unstudied.

In the first part of this study, I identified the primary source of nIgM. Using enzyme-linked immunosorbent spot (ELISPOT) assay, I determined that the majority of IgM Ab-secreting cells (ASCs) in naïve mice reside in the bone marrow (BM). Flow cytometric analysis of BM cells stained for intracellular IgM revealed that nIgM ASCs express IgM and the PC marker CD138 on their surface, but not the B1a cell marker CD5. By spinning these cells onto slides and staining them, following isolation by fluorescence-activated cell sorting (FACS), I found that they exhibit the typical morphological characteristics of terminally differentiated PCs. Transfer experiments demonstrated that BM nIgM PCs arise from a progenitor in the peritoneal cavity (PerC), but not isolated PerC B1a, B1b, or B2 cells. Immunoglobulin (Ig) gene sequence analysis and examination of B1-8i mice, which carry an Ig knockin that prohibits fetal B-cell development, indicated that nIgM PCs differentiate from fetal-lineage B cells. BrdU uptake experiments showed that the nIgM ASC compartment contains a substantial fraction of long-lived plasma cells (LLPCs). Finally, I demonstrated that nIgM PCs occupy a survival niche distinct from that used by IgG PCs.

In the second part of this dissertation, I characterized the unique survival niche of nIgM LLPCs, which maintain constitutive high titers of nIgM in the serum. By using genetically deficient or Ab-depleted mice, I found that neither T cells, type 2 innate lymphoid cells, nor mast cells, the three major hematopoietic producers of IL-5, were required for nIgM PC survival in the BM. However, IgM PCs associate strongly with IL-5-expressing BM stromal cells, which support their survival in vitro when stimulated. In vivo neutralization of IL-5 revealed that, like individual survival factors for IgG PCs, IL-5 is not the sole supporter of IgM PCs, but is likely one of several redundant molecules that together ensure uninterrupted signaling. Thus, the long-lived nIgM PC niche is not composed of hematopoietic sources of IL-5, but a stromal cell microenvironment that provides multiple redundant survival signals.

In the final part of my study, I identified and characterized the precursor of nIgM PCs, which I found in the first project to be resident in the PerC, but not a B1a, B1b, or B2 cell. By transferring PerC cells sorted based on expression of CD19, CD5, and CD11b, I found that only the CD19+CD5+CD11b- population contained cells capable of differentiating into nIgM PCs. Transfer of decreasing numbers of unfractionated PerC cells into Rag1 knockouts revealed an order-of-magnitude drop in the rate of serum IgM reconstitution between stochastically sampled pools of 106 and 3x105 PerC cells, suggesting that the CD19+CD5+CD11b- compartment comprises two cell types, and that interaction between the two necessary for nIgM-PC differentiation. By transferring neonatal liver, I determined that the early hematopoietic environment is required for nIgM PC precursors to develop. Using mice carrying a mutation that disturbs cKit expression, I also found that cKit appears to be required at a critical point near birth for the proper development of nIgM PC precursors.

The collective results of these studies demonstrate that nIgM is the product of BM-resident PCs, which differentiate from a PerC B cell precursor distinct from B1a cells, and survive long-term in a unique survival niche created by stromal cells. My work creates a new paradigm by which to understand nIgM, B1 cell, and PC biology.

Can prospect theory explain risk-seeking behavior by terminally ill patients?

Patients with life-threatening conditions sometimes appear to make risky treatment decisions as their condition declines, contradicting the risk-averse behavior predicted by expected utility theory. Prospect theory accommodates such decisions by describing how individuals evaluate outcomes relative to a reference point and how they exhibit risk-seeking behavior over losses relative to that point. The authors show that a patient's reference point for his or her health is a key factor in determining which treatment option the patient selects, and they examine under what circumstances the more risky option is selected. The authors argue that patients' reference points may take time to adjust following a change in diagnosis, with implications for predicting under what circumstances a patient may select experimental or conventional therapies or select no treatment.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Molecular mapping of movement-associated areas in the avian brain: a motor theory for vocal learning origin.

Vocal learning is a critical behavioral substrate for spoken human language. It is a rare trait found in three distantly related groups of birds-songbirds, hummingbirds, and parrots. These avian groups have remarkably similar systems of cerebral vocal nuclei for the control of learned vocalizations that are not found in their more closely related vocal non-learning relatives. These findings led to the hypothesis that brain pathways for vocal learning in different groups evolved independently from a common ancestor but under pre-existing constraints. Here, we suggest one constraint, a pre-existing system for movement control. Using behavioral molecular mapping, we discovered that in songbirds, parrots, and hummingbirds, all cerebral vocal learning nuclei are adjacent to discrete brain areas active during limb and body movements. Similar to the relationships between vocal nuclei activation and singing, activation in the adjacent areas correlated with the amount of movement performed and was independent of auditory and visual input. These same movement-associated brain areas were also present in female songbirds that do not learn vocalizations and have atrophied cerebral vocal nuclei, and in ring doves that are vocal non-learners and do not have cerebral vocal nuclei. A compilation of previous neural tracing experiments in songbirds suggests that the movement-associated areas are connected in a network that is in parallel with the adjacent vocal learning system. This study is the first global mapping that we are aware for movement-associated areas of the avian cerebrum and it indicates that brain systems that control vocal learning in distantly related birds are directly adjacent to brain systems involved in movement control. Based upon these findings, we propose a motor theory for the origin of vocal learning, this being that the brain areas specialized for vocal learning in vocal learners evolved as a specialization of a pre-existing motor pathway that controls movement.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.