Approximate Boltzmann Distributions for Nonreversible Markov Chains

While powerful theories for the analysis of reversible Markov chains have enabled significant mathematical advances, nonequilibrium phenomena dominate the sciences and nonequilibrium chains do not enjoy the same formal foundations. For instance, the stationary distributions of reversible chains are fundamentally simpler than those of nonreversible chains because they are Boltzmann distributions -- they can be expressed in terms of a purely local "free energy" landscape, in analogy with equilibrium statistical physics. In general, it is impossible to similarly represent the steady states of nonequilibrium physical systems in a purely local way. However, a series of recent works on rattling theory (e.g., Chvykov et al., Science (2021)) provides strong evidence that a broad class of such systems nevertheless exhibit "approximate Boltzmann distributions," which allow some aspects of the global distributions to be inferred, at least approximately, from local information. We formalize the main claims of this physical theory to identify its hidden assumptions and demonstrate its basis in the theory of continuous-time Markov chains. To do so, we decompose an arbitrary stationary distribution $\pi$ into its "local" part -- the exit rates $q$ out of each state -- and its "global" part -- the stationary distribution $\psi$ of the embedded "jump" chain. We explain a variety of experimental results by showing that, for a random state, $\log \pi$ and $-\log q$ are correlated to the extent that $\log \psi$ and $-\log q$ are correlated or the ratio of their variances is small. In particular, the predictions of rattling theory apply when the global part of $\pi$ varies over fewer scales than its local part. We use this fact to demonstrate classes of nonreversible chains with stationary distributions that are exactly of Boltzmann type.Comment: 14 pages, 1 figur

The Inherent Disadvantage of the Presidential Party in Midterm Congressional Elections

The almost inevitable midterm election loss suffered by the president's congressional party still lacks a complete explanation. It is argued here that the policy positions of the president help shape voters' perceptions of the positions of congressional candidates. Because the president implements policies before the midterm campaign begins, and because he has goals apart from winning seats in Congress, his party's candidates are at a disadvantage, relative to their opponents, in communicating the most favorable positions possible to their voters. This model of the midterm campaign not only explains midterm losses, but also accounts for rare failures of this phenomenon, as occurred in 1934

Presidential Coattails in Historical Perspective

It is agreed that the degree of association between the presidential and congressional election results is an important "Constitutional" variable. But the significance of this association depends on whether it is due to extraneous forces or to the personal attractiveness of the president. In this paper we give a statistical basis for determining the dependence of the vote for members of the House on the attractiveness of the presidential candidate. Further, it is shown that their dependence has decreased rather sharply and is currently at a historical low point

Coccidiomycosis infection of the patella mimicking a neoplasm - two case reports.

BackgroundCoccidioidomycosis is an endemic fungal infection in the southwestern of United States. Most infections are asymptomatic or manifest with mild respiratory complaints. Rare cases may cause extrapulmonary or disseminated disease. We report two cases of knee involvement that presented as isolated lytic lesions of the patella mimicking neoplasms.Case presentationThe first case, a 27 year-old immunocompetent male had progressive left anterior knee pain for four months. The second case was a 78 year-old male had left anterior knee pain for three months. Both of them had visited general physicians without conclusive diagnosis. A low attenuation lytic lesion in the patella was demonstrated on their image studies, and the initial radiologist's interpretation was suggestive of a primary bony neoplasm. The patients were referred for orthopaedic oncology consultation. The first case had a past episode of pulmonary coccioidomycosis 2 years prior, while the second case had no previous coccioidal infection history but lived in an endemic area, the central valley of California. Surgical biopsy was performed in both cases due to diagnostic uncertainty. Final pathologic examination revealed large thick walled spherules filled with endospores establishing the final diagnosis of extrapulmonary coccidioidomycosis.ConclusionsThough history and laboratory findings are supportive, definitive diagnosis still depends on growth in culture or endospores identified on histology. We suggest that orthopaedic surgeons and radiologists keep in mind that chronic fungal infections can mimic osseous neoplasm by imaging

Extra-Abdominal Desmoid Tumors Associated with Familial Adenomatous Polyposis

Extra-abdominal desmoid tumors are a significant cause of morbidity in patients with familial adenomatous polyposis syndrome. Understanding of the basic biology and natural history of these tumors has increased substantially over the past decade. Accordingly, medical and surgical management of desmoid tumors has also evolved. This paper analyzes recent evidence pertaining to the epidemiology, molecular biology, histopathology, screening, and treatment of extra-abdominal desmoid tumors associated with familial adenomatous polyposis syndrome

Presidential Coattails in Historical Perspective

It is agreed that the degree of association between the presidential and congressional election results is an important "Constitutional" variable. But the significance of this association depends on whether it is due to extraneous forces or to the personal attractiveness of the president. In this paper we give a statistical basis for determining the dependence of the vote for members of the House on the attractiveness of the presidential candidate. Further, it is shown that their dependence has decreased rather sharply and is currently at a historical low point

The Inherent Disadvantage of the Presidential Party in Midterm Congressional Elections

The almost inevitable midterm election loss suffered by the president's congressional party still lacks a complete explanation. It is argued here that the policy positions of the president help shape voters' perceptions of the positions of congressional candidates. Because the president implements policies before the midterm campaign begins, and because he has goals apart from winning seats in Congress, his party's candidates are at a disadvantage, relative to their opponents, in communicating the most favorable positions possible to their voters. This model of the midterm campaign not only explains midterm losses, but also accounts for rare failures of this phenomenon, as occurred in 1934

At-Risk Populations for Osteosarcoma: The Syndromes and Beyond

Osteosarcoma is the most common primary malignancy of bone. Most cases are sporadic without a known genetic or environmental cause. Heritable genetic predisposition syndromes are associated with a small percentage of osteosarcomas. Study of these rare disorders has provided insight into the molecular pathogenesis of osteosarcoma. Screening of at-risk families and surveillance of affected individuals for these syndromes may permit earlier diagnosis and more effective treatment of osteosarcoma in these populations. This paper reviews the genetic and clinical features of the known osteosarcoma predisposition syndromes