Renormalisation-induced phase transitions for unimodal maps

The thermodynamical formalism is studied for renormalisable maps of the interval and the natural potential $-t \log|Df|$. Multiple and indeed infinitely many phase transitions at positive $t$ can occur for some quadratic maps. All unimodal quadratic maps with positive topological entropy exhibit a phase transition in the negative spectrum.Comment: 14 pages, 2 figures. Revised following comments of referees. First page is blan

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

On the accuracy of solving confluent Prony systems

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as frequency estimation and nonlinear Fourier inversion. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes critical for the success of any particular application. We investigate the question of "maximal possible accuracy" of solving Prony-type systems, putting stress on the "local" behavior which approximates situations with low absolute measurement error. The accuracy estimates are formulated in very simple geometric terms, shedding some light on the structure of the problem. Numerical tests suggest that "global" solution techniques such as Prony's algorithm and ESPRIT method are suboptimal when compared to this theoretical "best local" behavior

Emulsifiers as Additives in Fats: Effect on Polymorphic Transformations and Crystal Properties of Fatty Acids and Triglycerides

The role of emulsifiers in polymorphic transformations of fats and fatty acids is treated in this paper. Their effect as crystal modifiers in solution-mediated transformations (in fatty acids) is compared to that of a dynamic controller of polymorphic transformations in triglycerides. The importance of chemical structure both in the hydrophilic and in the hydrophobic moieties of the emulsifier for an inhibitory effect on phase transitions has been emphasized. The emulsifier solubility and crystallization behavior in different solvents are probably the main factors affecting its ability to interfere with the kinetics of solution-mediated transformations. On the other hand, certain requirements for a specific chemical structure of the emulsifier which provides good structure compatibility, must be met in order to affect the kinetics and mechanism of solid-solid or melt-mediated transformations. A mechanism of emulsifier incorporation in the fat and its effect in delaying the polymorphic transformation of tristearin is proposed. It has been concluded that the presence of the emulsifier does not dictate the formation of any preferred polymorph but rather controls the mobility of the molecules and their facility to undergo polymorphic transformations. The relationship between polymorphism in fats and presence of additives plays a major role in the food industry, because of the serious quality implications involved in phase transitions

Secondary dentin formation mechanism: The effect of attrition

Human dentin consists of a primary layer produced during tooth formation in early child-hood and a second layer which first forms upon tooth eruption and continues throughout life, termed secondary dentin (SD). The effect of attrition on SD formation was considered to be confined to the area subjacent to attrition facets. However, due to a lack of three‐dimensional methodologies to demonstrate the structure of the SD, this association could not be determined. Therefore, in the current study, we aimed to explore the thickening pattern of the SD in relation to the amount of occlusal and interproximal attrition. A total of 30 premolars (50–60 years of age) with varying attrition rates were evaluated using micro‐computerized tomography. The results revealed thickening of the SD below the cementoenamel junction (CEJ), mostly in the mesial and distal aspects of the root (p < 0.05). The pattern of thickening under the tooth cervix, rather than in proximity to attrition facets, was consistent regardless of the attrition level. The amount of SD thickening mildly corre-lated with occlusal attrition (r = 0.577, p < 0.05) and not with interproximal attrition. The thickening of the SD below the CEJ coincided with previous finite element models, suggesting that this area is mostly subjected to stress due to occlusal loadings. Therefore, we suggest that the SD formation might serve as a compensatory mechanism aimed to strengthen tooth structure against deflection caused by mechanical loading. Our study suggests that occlusal forces may play a significant role in SD formation

Moment inversion problem for piecewise D-finite functions

We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation with polynomial coefficients on each continuity interval. Therefore, they may be specified by a finite amount of information. This reconstruction problem has practical importance in Signal Processing and other applications. It is somewhat of a ``folklore'' that the sequence of the moments of such ``piecewise D-finite''functions satisfies a linear recurrence relation of bounded order and degree. We derive this recurrence relation explicitly. It turns out that the coefficients of the differential operator which annihilates every piece of the function, as well as the locations of the discontinuities, appear in this recurrence in a precisely controlled manner. This leads to the formulation of a generic algorithm for reconstructing a piecewise D-finite function from its moments. We investigate the conditions for solvability of the resulting linear systems in the general case, as well as analyze a few particular examples. We provide results of numerical simulations for several types of signals, which test the sensitivity of the proposed algorithm to noise

p53 Plays a Role in Mesenchymal Differentiation Programs, in a Cell Fate Dependent Manner

Background: The tumor suppressor p53 is an important regulator that controls various cellular networks, including cell differentiation. Interestingly, some studies suggest that p53 facilitates cell differentiation, whereas others claim that it suppresses differentiation. Therefore, it is critical to evaluate whether this inconsistency represents an authentic differential p53 activity manifested in the various differentiation programs. Methodology/Principal Findings: To clarify this important issue, we conducted a comparative study of several mesenchymal differentiation programs. The effects of p53 knockdown or enhanced activity were analyzed in mouse and human mesenchymal cells, representing various stages of several differentiation programs. We found that p53 downregulated the expression of master differentiation-inducing transcription factors, thereby inhibiting osteogenic, adipogenic and smooth muscle differentiation of multiple mesenchymal cell types. In contrast, p53 is essential for skeletal muscle differentiation and osteogenic re-programming of skeletal muscle committed cells. Conclusions: These comparative studies suggest that, depending on the specific cell type and the specific differentiatio

Stress-Induced C/EBP Homology Protein (CHOP) Represses MyoD Transcription to Delay Myoblast Differentiation

When mouse myoblasts or satellite cells differentiate in culture, the expression of myogenic regulatory factor, MyoD, is downregulated in a subset of cells that do not differentiate. The mechanism involved in the repression of MyoD expression remains largely unknown. Here we report that a stress-response pathway repressing MyoD transcription is transiently activated in mouse-derived C2C12 myoblasts growing under differentiation-promoting conditions. We show that phosphorylation of the α subunit of the translation initiation factor 2 (eIF2α) is followed by expression of C/EBP homology protein (CHOP) in some myoblasts. ShRNA-driven knockdown of CHOP expression caused earlier and more robust differentiation, whereas its constitutive expression delayed differentiation relative to wild type myoblasts. Cells expressing CHOP did not express the myogenic regulatory factors MyoD and myogenin. These results indicated that CHOP directly repressed the transcription of the MyoD gene. In support of this view, CHOP associated with upstream regulatory region of the MyoD gene and its activity reduced histone acetylation at the enhancer region of MyoD. CHOP interacted with histone deacetylase 1 (HDAC1) in cells. This protein complex may reduce histone acetylation when bound to MyoD regulatory regions. Overall, our results suggest that the activation of a stress pathway in myoblasts transiently downregulate the myogenic program

The Shortest Isoform of Dystrophin (Dp40) Interacts with a Group of Presynaptic Proteins to Form a Presumptive Novel Complex in the Mouse Brain

Duchenne muscular dystrophy (DMD) causes cognitive impairment in one third of the patients, although the underlying mechanisms remain to be elucidated. Recent studies showed that mutations in the distal part of the dystrophin gene correlate well with the cognitive impairment in DMD patients, which is attributed to Dp71. The study on the expression of the shortest isoform, Dp40, has not been possible due to the lack of an isoform specific antibody. Dp40 has the same promoter as that found in Dp71 and lacks the normal C-terminal end of Dp427. In the present study, we have raised polyclonal antibody against the N-terminal sequence common to short isoforms of dystrophin, including Dp40, and investigated the expression pattern of Dp40 in the mouse brain. Affinity chromatography with this antibody and the consecutive LC-MS/MS analysis on the interacting proteins revealed that Dp40 was abundantly expressed in synaptic vesicles and interacted with a group of presynaptic proteins, including syntaxin1A and SNAP25, which are involved in exocytosis of synaptic vesicles in neurons. We thus suggest that Dp40 may form a novel protein complex and play a crucial role in presynaptic function. Further studies on these aspects of Dp40 function might provide more insight into the molecular mechanisms of cognitive impairment found in patients with DMD