The Ising Partition Function: Zeros and Deterministic Approximation

We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs that is valid over the entire range of parameters $\beta$ (the interaction) and $\lambda$ (the external field), except for the case $\vert{\lambda}\vert=1$ (the "zero-field" case). A randomized algorithm (FPRAS) for all graphs, and all $\beta,\lambda$, has long been known. Unlike most other deterministic approximation algorithms for problems in statistical physics and counting, our algorithm does not rely on the "decay of correlations" property. Rather, we exploit and extend machinery developed recently by Barvinok, and Patel and Regts, based on the location of the complex zeros of the partition function, which can be seen as an algorithmic realization of the classical Lee-Yang approach to phase transitions. Our approach extends to the more general setting of the Ising model on hypergraphs of bounded degree and edge size, where no previous algorithms (even randomized) were known for a wide range of parameters. In order to achieve this extension, we establish a tight version of the Lee-Yang theorem for the Ising model on hypergraphs, improving a classical result of Suzuki and Fisher.Comment: clarified presentation of combinatorial arguments, added new results on optimality of univariate Lee-Yang theorem

Contrasting mechanisms of penile urethral formation in mouse and human.

This paper addresses the developmental mechanisms of formation of the mouse and human penile urethra and the possibility that two disparate mechanisms are at play. It has been suggested that the entire penile urethra of the mouse forms via direct canalization of the endodermal urethral plate. While this mechanism surely accounts for development of the proximal portion of the mouse penile urethra, we suggest that the distal portion of the mouse penile urethra forms via a series of epithelial fusion events. Through review of the recent literature in combination with new data, it is unlikely that the entire mouse urethra is formed from the endodermal urethral plate due in part to the fact that from E14 onward the urethral plate is not present in the distal aspect of the genital tubercle. Formation of the distal portion of the mouse urethra receives substantial contribution from the preputial swellings that form the preputial-urethral groove and subsequently the preputial-urethral canal, the later of which is subdivided by a fusion event to form the distal portion of the mouse penile urethra. Examination of human penile development also reveals comparable dual morphogenetic mechanisms. However, in the case of human, direct canalization of the urethral plate occurs in the glans, while fusion events are involved in formation of the urethra within the penile shaft, a pattern exactly opposite to that of the mouse. The highest incidence of hypospadias in humans occurs at the junction of these two different developmental mechanisms. The relevance of the mouse as a model of human hypospadias is discussed

Smart DC/DC Wall Plug Design For The DC House Project

The present day duplex wall receptacle in the United States provides 120Vrms AC at 60Hz, which comes from a standard set for AC loads by the National Electrical Manufacturers Association. With a DC system, such as what is used in the DC House project currently being developed at Cal Poly, providing DC power to DC loads presents a technical challenge due to the different required DC operating voltages of the loads. This thesis entails the design and construction of a Smart DC/DC Wall Plug, which can automatically adjust its output voltage to match any required DC load voltages. In the DC House implementation, renewable energy sources generate power to feed a 48V DC Bus. The Smart DC/DC Wall Plug converts power from the 48V bus to the appropriate voltage and power levels needed by the DC loads. The Smart DC/DC Wall Plug relies on load current detection, and uses a 10-bit digital potentiometer and a programmable current DAC to adjust the feedback network, thereby changing the output voltage. A dual channel 100W PCB prototype utilizing a STMF302R8 microcontroller is implemented for this design while confining to the NEMA wall outlet form factor. Results of hardware test verify the functionality of the Smart DC/DC Wall Plug in producing the required DC load voltages. Technical issues during the development of the Smart DC/DC Wall Plug will be described, along with suggestions to further improve from the current design

Clitoral development in the mouse and human.

The goal of this report is (a) to provide the first detailed description of mouse clitoral development, and (b) to compare mouse and human clitoral development. For this purpose, external genitalia of female mice were examined by wholemount microscopy, histology and immunohistochemistry from 14 days of gestation to 10 days postnatal. Human clitoral development was examined by these techniques as well as by scanning electron microscopy and optical projection tomography from 8 to 19 weeks of gestation. The adult mouse clitoris is an internal organ defined by a U-shaped clitoral lamina whose development is associated with the prenatal medial and distal growth of the female preputial swellings along the sides of the genital tubercle to form the circumferential preputial lamina. Regression of the ventral aspect of the preputial lamina leads to formation of the U-shaped clitoral lamina recognized as early as 17 days of gestation. While the adult U-shaped mouse clitoral lamina is closely associated with the vagina, and it appears to be completely non-responsive to estrogen as opposed to the highly estrogen-responsive vaginal epithelium. The prominent perineal appendage in adult females is prepuce, formed via fusion of the embryonic preputial swellings and is not the clitoris. The human clitoris is in many respects a smaller anatomic version of the human penis having all of the external and internal elements except the urethra. The human clitoris (like the human penis) is derived from the genital tubercle with the clitoral glans projecting into the vaginal vestibule. Adult morphology and developmental processes are virtually non-comparable in the mouse and human clitoris

Development of the human bladder and ureterovesical junction.

The urinary bladder collects urine from the kidneys and stores it until the appropriate moment for voiding. The trigone and ureterovesical junctions are key to bladder function, by allowing one-way passage of urine into the bladder without obstruction. Embryological development of these structures has been studied in multiple animal models as well as humans. In this report we review the existing literature on bladder development and cellular signalling with particular focus on bladder development in humans. The bladder and ureterovesical junction form primarily during the fourth to eighth weeks of gestation, and arise from the primitive urogenital sinus following subdivision of the cloaca. The bladder develops through mesenchymal-epithelial interactions between the endoderm of the urogenital sinus and mesodermal mesenchyme. Key signalling factors in bladder development include shh, TGF-β, Bmp4, and Fgfr2. A concentration gradient of shh is particularly important in development of bladder musculature, which is vital to bladder function. The ureterovesical junction forms from the interaction between the Wolffian duct and the bladder. The ureteric bud arises from the Wolffian duct and is incorporated into the developing bladder at the trigone. It was previously thought that the trigonal musculature developed primarily from the Wolffian duct, but it has been shown to develop primarily from bladder mesenchyme. Following emergence of the ureters from the Wolffian ducts, extensive epithelial remodelling brings the ureters to their final trigonal positions via vitamin A-induced apoptosis. Perturbation of this process is implicated in clinical obstruction or urine reflux. Congenital malformations include ureteric duplication and bladder exstrophy

Correlation decay and partition function zeros: Algorithms and phase transitions

We explore connections between the phenomenon of correlation decay and the location of Lee-Yang and Fisher zeros for various spin systems. In particular we show that, in many instances, proofs showing that weak spatial mixing on the Bethe lattice (infinite $\Delta$-regular tree) implies strong spatial mixing on all graphs of maximum degree $\Delta$ can be lifted to the complex plane, establishing the absence of zeros of the associated partition function in a complex neighborhood of the region in parameter space corresponding to strong spatial mixing. This allows us to give unified proofs of several recent results of this kind, including the resolution by Peters and Regts of the Sokal conjecture for the partition function of the hard core lattice gas. It also allows us to prove new results on the location of Lee-Yang zeros of the anti-ferromagnetic Ising model. We show further that our methods extend to the case when weak spatial mixing on the Bethe lattice is not known to be equivalent to strong spatial mixing on all graphs. In particular, we show that results on strong spatial mixing in the anti-ferromagnetic Potts model can be lifted to the complex plane to give new zero-freeness results for the associated partition function. This extension allows us to give the first deterministic FPTAS for counting the number of $q$-colorings of a graph of maximum degree $\Delta$ provided only that $q\ge 2\Delta$. This matches the natural bound for randomized algorithms obtained by a straightforward application of Markov chain Monte Carlo. We also give an improved version of this result for triangle-free graphs

Fisher Zeros and Correlation Decay in the Ising Model

The Ising model originated in statistical physics as a means of studying phase transitions in magnets, and has been the object of intensive study for almost a century. Combinatorially, it can be viewed as a natural distribution over cuts in a graph, and it has also been widely studied in computer science, especially in the context of approximate counting and sampling. In this paper, we study the complex zeros of the partition function of the Ising model, viewed as a polynomial in the "interaction parameter"; these are known as Fisher zeros in light of their introduction by Fisher in 1965. While the zeros of the partition function as a polynomial in the "field" parameter have been extensively studied since the classical work of Lee and Yang, comparatively little is known about Fisher zeros. Our main result shows that the zero-field Ising model has no Fisher zeros in a complex neighborhood of the entire region of parameters where the model exhibits correlation decay. In addition to shedding light on Fisher zeros themselves, this result also establishes a formal connection between two distinct notions of phase transition for the Ising model: the absence of complex zeros (analyticity of the free energy, or the logarithm of the partition function) and decay of correlations with distance. We also discuss the consequences of our result for efficient deterministic approximation of the partition function. Our proof relies heavily on algorithmic techniques, notably Weitz\u27s self-avoiding walk tree, and as such belongs to a growing body of work that uses algorithmic methods to resolve classical questions in statistical physics

Trade, foreign direct investment and economic growth in Asian economies

Despite the increasing role of foreign direct investment (FDI) in economic development, very limited research has been carried out on the causal links between trade, FDI and economic growth in Asian economies. This study examines empirically the interplay between exports, imports, FDI and economic growth for nine Asian economies by conducting multivariate causality tests in the VECM framework. The results reveal two-way causal connections between trade, inward FDI, inward merger and acquisitions (M&As), and growth for most of the sample economies. There is a unidirectional causal link running from outward M&As to growth and trade. These findings suggest that export expansion, import liberalisation, FDI inflows and inward M&As are integral elements of the growth process in Asian economies

Androgen-independent events in penile development in humans and animals.

The common view on penile development is that it is androgen-dependent, based first and foremost on the fact that the genital tubercle forms a penis in males and a clitoris in females. However, critical examination of the complex processes involved in human penile development reveals that many individual steps in development of the genital tubercle are common to both males and females, and thus can be interpreted as androgen-independent. For certain developmental events this conclusion is bolstered by observations in androgen-insensitive patients and androgen receptor mutant mice. Events in genital tubercle development that are common to human males and females include: formation of (a) the genital tubercle, (b) the urethral plate, (c) the urethral groove, (d) the glans, (e) the prepuce and (f) the corporal body. For humans 6 of 13 individual developmental steps in penile development were interpreted as androgen-independent. For mice 5 of 11 individual developmental steps were found to be androgen-independent, which were verified through analysis of androgen-insensitive mutants. Observations from development of external genitalia of other species (moles and spotted hyena) provide further examples of androgen-independent events in penile development. These observations support the counter-intuitive idea that penile development involves both androgen-independent and androgen-dependent processes