Graphs without proper subgraphs of minimum degree 3 and short cycles

We study graphs on n vertices which have 2n−2 edges and no proper induced subgraphs of minimum degree 3. Erdős, Faudree, Gyárfás, and Schelp conjectured that such graphs always have cycles of lengths 3,4,5,...,C(n) for some function C(n) tending to in finity. We disprove this conjecture, resolve a related problem about leaf-to-leaf path lengths in trees, and characterize graphs with n vertices and 2n−2 edges, containing no proper subgraph of minimum degree 3

Strong Ramsey games: Drawing on an infinite board

Consider the following strong Ramsey game. Two players take turns in claiming a previously unclaimed edge of the complete graph on n vertices until all edges have been claimed. The first player to build a copy of K5 is declared the winner of the game. If none of the players win, then the game ends in a draw. A simple strategy stealing argument shows that the second player cannot expect to ever win this game. Moreover, for sufficiently large n, it follows from Ramsey’s Theorem that the game cannot end in a draw and is thus a first player win. A famous question of Beck asks whether the minimum number of moves needed for the first player to win this game on Kn grows with n. This seems unlikely but is still wide open. A striking equivalent formulation of this question is whether the same game played on the infinite complete graph is a first player win or a draw. The target graph of the strong Ramsey game does not have to be K5, it can be any predetermined fixed graph. In fact, it can even be a k-uniform hypergraph (and then the game is played on the infinite k-uniform hypergraph). Since strategy stealing and Ramsey’s Theorem still apply, one can ask the same question: is this game a first player win or a draw? The same intuition which lead most people (including the authors) to believe that the K5 strong Ramsey game on the infinite board is a first player win, would also lead one to believe that the H strong Ramsey game on the infinite board is a first player win for any uniform hypergraph H. However, in this paper we construct a 5-uniform hypergraph for which the corresponding game is a draw

Graphs without proper subgraphs of minimum degree 3 and short cycles

We study graphs on n vertices which have 2n−2 edges and no proper induced subgraphs of minimum degree 3. Erdős, Faudree, Gyárfás, and Schelp conjectured that such graphs always have cycles of lengths 3,4,5,…,C(n) for some function C(n) tending to infinity. We disprove this conjecture, resolve a related problem about leaf-to-leaf path lengths in trees, and characterize graphs with n vertices and 2n−2 edges, containing no proper subgraph of minimum degree 3

Synovial incorporation of polyacrylamide hydrogel after injection into normal and osteoarthritic animal joints

Polyacrylamide hydrogel (PAAG) is a non-toxic, non-degradable synthetic product, used for years in the augmentation of soft tissues. Preliminary results in animals and humans have suggested long-lasting beneficial effects on symptoms of osteoarthritis (OA). The aim of this histopathological study was to investigate whether intra-articular injection of PAAG is integrated into synovial tissue in normal and OA animal joints, and if this integration is sustained.(A) A prospective, controlled, longitudinal study of normal knee joints injected with PAAG was performed in 10 rabbits, following the animals up to 1 year, and (B) a post mortem examination was carried out up to 2 years post-injection on 18 horse joints which had previously been treated with 1-2 injections of 2 ml PAAG for clinically and radiologically diagnosed OA.Integration of the injected gel was evident at day 10 in the rabbit and by day 14 in the horse, with proliferation and invasion of synovial cells into the gel. By day 90 in rabbit joints and day 30 in horse joints, the gel had formed a sub-synovial layer, which was traversed by thin strands of connective tissue with vessels and covered by a synovial lining facing the joint cavity. This histological appearance persisted up to 2 years post-injection in horse joints.Intra-articular injection of PAAG results in a stable, long-lasting sub-synovial layer of gel traversed with thin strands of connective tissue. Further studies to explore potential effects on synovial inflammation and pain are warranted

Strong Ramsey games: drawing on an infinite board

We consider the strong Ramsey-type game R(k)(H,ℵ0), played on the edge set of the infinite complete k-uniform hypergraph KkN. Two players, called FP (the first player) and SP (the second player), take turns claiming edges of K^k_N with the goal of building a copy of some finite predetermined k-uniform hypergraph H. The first player to build a copy of H wins. If no player has a strategy to ensure his win in finitely many moves, then the game is declared a draw. In this paper, we construct a 5-uniform hypergraph H such that R(5)(H,ℵ0) is a draw. This is in stark contrast to the corresponding finite game R(5)(H,n), played on the edge set of K5n. Indeed, using a classical game-theoretic argument known as \emph{strategy stealing} and a Ramsey-type argument, one can show that for every k-uniform hypergraph G, there exists an integer n0 such that FP has a winning strategy for R(k)(G,n) for every n≥n0

TGF-β receptor expression and binding in rat mesangial cells: Modulation by glucose and cyclic mechanical strain

TGF-β receptor expression and binding in rat mesangial cells: Modulation by glucose and cyclic mechanical strain.BackgroundTransforming growth factor-β (TGF-β) is a causal factor in experimental glomerulosclerosis, and it mediates the increased extracellular matrix (ECM) accumulation that occurs in cultured mesangial cells (MCs) exposed to high glucose concentrations and cyclic mechanical strain. This change is associated with increased levels of TGF-β, but may also involve alterations in receptor expression and binding.MethodsRat MCs cultured in media containing either 8 or 35 mM glucose were seeded into culture plates with elastin-coated flexible bottoms. Thereafter, they were subjected to cyclic stretch or static conditions and then examined for125I-TGF-β1 binding and expression of TGF-β receptors at the gene and protein levels.ResultsKinetic studies showed that MCs bound TGF-β1 in a time- and concentration-dependent manner, expressing 6800 high-affinity receptors per cell, with an apparent dissociation constant (Kd) of 15.4 pM, while cross-linking analysis identified three TGF-β receptors (βR) corresponding to βRI, βRII, and βRIII of 54, 73, and 200 kDa, respectively. Immunocytochemical studies of βRI and βRII protein revealed MC expression in a homogeneous, punctate distribution, whereas Northern analysis demonstrated the presence of the corresponding mRNAs. Exposure to cyclic stretching significantly increased (10%) the overall number of TGF-β receptors, whereas ligands associated with βRs I, II, and III also increased (25 to 50%). The finding of increased (30 to 40%) βRI and βRII transcript levels and immunoreactive protein (163 and 59%, respectively) in the absence of significant changes in the apparent Kd indicated that stretch-induced binding was the result of increased receptor synthesis and expression and not due to a change in binding affinity. In a similar, but more dramatic fashion, exposure to high glucose also elevated (50%) the receptor number, as well as the amount of ligands associated with βRs I, II, and III (100 to 250%). This same treatment also increased the levels of βRI and βRII mRNA (30 to 40%) and the immunoreactive protein (82 and 82%, respectively), without significantly altering the binding affinity of the receptor. A concerted or synergistic effect of both stimuli was not evidenced.ConclusionThese results suggest that the modulation of TGF-β receptors may be an additional control point in mediating the glucose- and mechanical force-induced increase in ECM deposition by MCs

Below the Belt? Territory and Development in China’s International Rise

China’s internationalization has been heralded by some as a new era of South–South cooperation. Yet such framings of development are pitched at an abstract space of the ‘global South’ which conceals more than it reveals. With some theory moving towards ontologies of ‘global development’, we need to capture both the connectedness and the local specificity of increasingly diffuse processes. This article sets out a more fine-grained understanding of how political territories and processes are imagined and produced by and through China’s internationalization, focusing on infrastructure as a ‘technology’ of territorialization. Much of the focus on China’s internationalization has been on state-to-state relations, but this obscures the ‘omni-channel politics’ that China practises. Using a critical literature review and illustrative case study, this article develops the idea of omni-channel politics to posit a view of ‘twisted’ territories in which political processes and development outcomes are more complex and contingent

Ultrasound-evoked immediate early gene expression in the brainstem of the Chinese torrent frog, Odorrana tormota

The concave-eared torrent frog, Odorrana tormota, has evolved the extraordinary ability to communicate ultrasonically (i.e., using frequencies > 20 kHz), and electrophysiological experiments have demonstrated that neurons in the frog’s midbrain (torus semicircularis) respond to frequencies up to 34 kHz. However, at this time, it is unclear which region(s) of the torus and what other brainstem nuclei are involved in the detection of ultrasound. To gain insight into the anatomical substrate of ultrasound detection, we mapped expression of the activity-dependent gene, egr-1, in the brain in response to a full-spectrum mating call, a filtered, ultrasound-only call, and no sound. We found that the ultrasound-only call elicited egr-1 expression in the superior olivary and principal nucleus of the torus semicircularis. In sampled areas of the principal nucleus, the ultrasound-only call tended to evoke higher egr-1 expression than the full-spectrum call and, in the center of the nucleus, induced significantly higher egr-1 levels than the no-sound control. In the superior olivary nucleus, the full-spectrum and ultrasound-only calls evoked similar levels of expression that were significantly greater than the control, and egr-1 induction in the laminar nucleus showed no evidence of acoustic modulation. These data suggest that the sampled areas of the principal nucleus are among the regions sensitive to ultrasound in this species

Mechanics of the exceptional anuran ear

The anuran ear is frequently used for studying fundamental properties of vertebrate auditory systems. This is due to its unique anatomical features, most prominently the lack of a basilar membrane and the presence of two dedicated acoustic end organs, the basilar papilla and the amphibian papilla. Our current anatomical and functional knowledge implies that three distinct regions can be identified within these two organs. The basilar papilla functions as a single auditory filter. The low-frequency portion of the amphibian papilla is an electrically tuned, tonotopically organized auditory end organ. The high-frequency portion of the amphibian papilla is mechanically tuned and tonotopically organized, and it emits spontaneous otoacoustic emissions. This high-frequency portion of the amphibian papilla shows a remarkable, functional resemblance to the mammalian cochlea

Effects of Noise Bandwidth and Amplitude Modulation on Masking in Frog Auditory Midbrain Neurons

Natural auditory scenes such as frog choruses consist of multiple sound sources (i.e., individual vocalizing males) producing sounds that overlap extensively in time and spectrum, often in the presence of other biotic and abiotic background noise. Detection of a signal in such environments is challenging, but it is facilitated when the noise shares common amplitude modulations across a wide frequency range, due to a phenomenon called comodulation masking release (CMR). Here, we examined how properties of the background noise, such as its bandwidth and amplitude modulation, influence the detection threshold of a target sound (pulsed amplitude modulated tones) by single neurons in the frog auditory midbrain. We found that for both modulated and unmodulated masking noise, masking was generally stronger with increasing bandwidth, but it was weakened for the widest bandwidths. Masking was less for modulated noise than for unmodulated noise for all bandwidths. However, responses were heterogeneous, and only for a subpopulation of neurons the detection of the probe was facilitated when the bandwidth of the modulated masker was increased beyond a certain bandwidth – such neurons might contribute to CMR. We observed evidence that suggests that the dips in the noise amplitude are exploited by TS neurons, and observed strong responses to target signals occurring during such dips. However, the interactions between the probe and masker responses were nonlinear, and other mechanisms, e.g., selective suppression of the response to the noise, may also be involved in the masking release