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For positive integers $n,r,s$ with $r > s$ , the set-coloring Ramsey number $R(n;r,s)$ is the minimum $N$ such that if every edge of the complete graph $K_{N}$ receives a set of $s$ colors from a palette of $r$ colors, then there is a subset of $n$ vertices where all of the edges between them receive a common color. If $n$ is fixed and $\frac {s}{r}$ is less than and bounded away from $1-\frac {1}{n-1}$ , then $R(n;r,s)$ is known to grow exponentially in $r$ , while if $\frac {s}{r}$ is greater than and bounded away from $1-\frac {1}{n-1}$ , then $R(n;r,s)$ is bounded. Here we prove bounds for $R(n;r,s)$ in the intermediate range where $\frac {s}{r}$ is close to $1 - \frac {1}{n-1}$ by establishing a connection to the maximum size of error-correcting codes near the zero-rate threshold.

We show that in any two‐coloring of the positive integers there is a color for which the set of positive integers that can be represented as a sum of distinct elements with this color has upper logarithmic density at least (2+3)/4$(2+\sqrt {3})/4$and this is best possible. This answers a 40‐year‐old question of Erdős.

The q-color Ramsey number of a k-uniform hypergraph G,  denoted r(G; q), is the minimum integer Nsuch that any coloring of the edges of the complete k-uniform hypergraph on Nvertices contains a monochromatic copy of G. The study of these numbers is one of the most central topics in combinatorics. One natural question, which for triangles goes back to the work of Schur in 1916, is to determine the behavior of r(G; q) for fixed Gand qtending to infinity. In this paper, we study this problem for 3-uniform hypergraphs and determine the tower height of r(G; q) as a function of q. More precisely, given a hypergraph G, we determine when r(G; q) behaves polynomially, exponentially or double exponentially in q. This answers a question of Axenovich, Gyárfás, Liu and Mubayi.

We prove that the discrepancy of arithmetic progressions in the d‐dimensional grid {1,⋯,N}d$\lbrace 1, \dots, N\rbrace ^d$is within a constant factor depending only on dof Nd2d+2$N^{\frac{d}{2d+2}}$. This extends the case d=1$d=1$, which is a celebrated result of Roth and of Matoušek and Spencer, and removes the polylogarithmic factor from the previous upper bound of Valkó from about two decades ago. We further prove similarly tight bounds for grids of differing side lengths in many cases.

Absurdist accounts of life’s meaning posit that life is absurd because our pretensions regarding its meaning conflict with the actual or perceived reality of the situation. Relationary accounts posit that contingent things gain their meaning only from their relationship to other meaningful things. I take a detailed look at the two types of account, and, proceeding under the assumption that they are correct, combine them to see what the implications of such a combination might be. I conclude that another way of looking at the absurdity of life is to see it as a conflict between our dual beliefs that there exist intrinsically meaningful contingent things, and that contingent things may only gain their meaning extrinsically through their relationships to other meaningful things. In this way, I provide another lens through which feelings of life’s absurdity may be interpreted and analysed: as the conflict between the simultaneous beliefs in both intrinsically and relationally meaningful contingent things. Looking through this lens gives us an entirely different framework for analysing life’s absurdity than that which Nagel described in 1971, providing opportunity for more potential avenues of analysis and discussion.

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The COVID-19 pandemic has exacerbated the flaws in the U.S. employer-based health insurance system, magnified racial disparities in health and health care, and overwhelmed the country’s underfunded public health infrastructure. These are the same systematic failures that have always harmed and killed the nation’s most vulnerable. While everyone wishes for an end to this national tragedy, the authors believe a new normal must be defined for the postpandemic period.In the postpandemic period, policies that were once labeled radical and impossible will be urgent and necessary. Examples of such policies include providing universal health care, dismantling the structures that propagate racism and injustice, and reinvesting in public health. Previous research by the authors has shown that their medical student colleagues recognize that it is their responsibility to address policies that harm patients and to support reforms at the scale the authors propose. This commitment to a better future is reflected in the widespread mobilization of medical students seen across the United States. Recognizing that the old normal is unsustainable, the authors call on those who previously benefited from the status quo to instead seek a new postpandemic normal that works for all.

Taxes generated from fuel sales represent an important source of revenue throughout North America and are broadly used with other sources to maintain and develop transportation networks and associated infrastructure. Historically, these taxes have performed well in providing a secure source of revenue. However, recent factors such as improved vehicle fleet efficiency and declining vehicle kilometers traveled (VKT) on a per vehicle and per capita basis affect the volume of fuel sold and threaten the security of existing sources of revenue generated from fuel taxes. Notwithstanding the obvious environmental benefits to which these factors contribute, a need remains to ensure that revenue streams are able to keep pace with funding requirements, given that auto ownership continues to rise, which places pressure on total VKT. The result is a decoupling of road usage and the main source of road user payments. The traditional solution to maintaining or growing revenue streams in the region of Metro Vancouver, British Columbia, Canada, has been to increase the fuel tax. However, the decoupling problem is intensified in the region because of the proximity to the border with the United States, where fuel price differentials are placing pressure on such solutions. This paper explores a number of recent trends that affect fuel sales in Metro Vancouver. Revenue implications are outlined, and policy recommendations are made to strengthen the link between road usage and road user payments.

Taxes generated from fuel sales represent an important source of revenue throughout North America and are broadly used with other sources to maintain and develop transportation networks and associated infrastructure. Historically, these taxes have performed well in providing a secure source of revenue. However, recent factors such as improved vehicle fleet efficiency and declining vehicle kilometers traveled (VKT) on a per vehicle and per capita basis affect the volume of fuel sold and threaten the security of existing sources of revenue generated from fuel taxes. Notwithstanding the obvious environmental benefits to which these factors contribute, a need remains to ensure that revenue streams are able to keep pace with funding requirements, given that auto ownership continues to rise, which places pressure on total VKT. The result is a decoupling of road usage and the main source of road user payments. The traditional solution to maintaining or growing revenue streams in the region of Metro Vancouver, British Columbia, Canada, has been to increase the fuel tax. However, the decoupling problem is intensified in the region because of the proximity to the border with the United States, where fuel price differentials are placing pressure on such solutions. This paper explores a number of recent trends that affect fuel sales in Metro Vancouver. Revenue implications are outlined, and policy recommendations are made to strengthen the link between road usage and road user payments.

Introduction. Silica nanoparticles (SiNPs) released during the burning of sugarcane have been postulated to have a role in chronic kidney disease of unknown etiology. We tested the hypothesis that pristine SiNPs of the size present in sugarcane might cause chronic kidney injury when administered through the lung in rats. Methods. We administered 200 nm or 300 nm amorphous SiNPs twice weekly (4 mg/dose) or vehicle by oropharyngeal aspiration for 13 weeks to rats followed by sacrifice after an additional 13 weeks (26 weeks total). Tissues were evaluated for presence of SiNPs and evidence of histologic injury. Results. Both sizes of SiNPs caused kidney damage, with early tubular injury and inflammation (at week 13) that continued to inflammation and chronic fibrosis at week 26 despite discontinuing the SiNP administration. Both sizes of SiNPs caused local inflammation in the lung and kidney and were detected in the serum and urine at week 13, and the 200 nm particles also localized to the kidney with no evidence of retention of the 300 nm particles. At week 26 there was some clearance of the 200 nm silica from the kidneys, and urinary levels of SiNPs were reduced but still significant in both the 200 and 300 nm exposed rats. Conclusions: Inhaled SiNPs causes chronic kidney injury that progresses despite stopping the SiNP administration. These findings are consistent with the hypothesis that human exposure to amorphous silica nanoparticles found in burned sugarcane fields could have a participatory role in chronic kidney disease of unknown etiology.

The Ramsey multiplicity M(G;n) of a graph Gis the minimum number of monochromatic copies of Gover all 2‐colorings of the edges of the complete graph Kn. For a graph Gwith aautomorphisms, ν vertices, and Eedges, it is natural to define the Ramsey multiplicity constant C(G) to be $\lim_{{n} \to \infty} {M}(G;n){a/v}!{n \choose v}$, which is the limit of the fraction of the total number of copies of Gwhich must be monochromatic in a 2‐coloring of the edges of Kn. In 1980, Burr and Rosta showed that 0 ≥ C(G) ≤ 21−Efor all graphs G, and conjectured that this upper bound is tight. Counterexamples of Burr and Rosta's conjecture were first found by Sidorenko and Thomason independently. Later, Clark proved that there are graphs Gwith Eedges and 2E−1C(G) arbitrarily small. We prove that for each positive integer E, there is a graph Gwith Eedges and C(G) ≤ E−E/2 + o(E). © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 89–98, 2008

We write H→ Gif every 2‐coloring of the edges of graph Hcontains a monochromatic copy of graph G. A graph His G‐minimalif H→ G, but for every proper subgraph H′ of H, H′ ↛ G. We define s(G) to be the minimum ssuch that there exists a G‐minimal graph with a vertex of degree s. We prove that s(Kk) = (k− 1)2and s(Ka,b) = 2 min(a,b) − 1. We also pose several related open problems. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 167–177, 2007

Abstract??Letm(n) be the maximum integer such that every partially ordered setPwithnelements contains two disjoint subsetsAandB, each with cardinalitym(n), such that either every element ofAis greater than every element ofBor every element ofAis incomparable with every element ofB. We prove that$m(n)=\theta\left(\frac{n}{\log n}\right)$. Moreover, for fixed?? (0,1) andnsufficiently large, we construct a partially ordered setPwithnelements such that no element ofPis comparable with$n^{\varepsilon } $other elements ofPand for every two disjoint subsetsAandBofPeach with cardinality at least$\frac{14n}{\epsilon\log_2 n}$, there is an element ofAthat is comparable with an element ofB.

• Long-latency event-related potentials (P300) were assessed in patients wth early probable Alzheimer's disease (AD), age-matched controls, and young adults during a task that imposed various degrees of demand on memory. Although patients with AD did not differ from age-matched controls when one item had to be remembered, their P300 potential was dramatically reduced in amplitude or absent with increasing memory load. Aged controls did not differ from young adults on this mesuer. P300 latency, however, did not differentiate patients with AD. Thus, electrophysiological abnormalities detected in the context of mnemonic demand may provide a sensitive marker of the early stages of probable AD.

We surveyed 522 consecutive patients from a dementia clinic to assess duration of driving after disease onset and instances of unsafe motor vehicle operation in the preceding 6 months. Among the 333 patients licensed to drive at the onset of dementia, the median duration of driving after onset was 28.6 months. Patients with a clinical diagnosis of Alzheimer's disease drove significantly longer than those with other dementia syndromes. Of the 93 patients still driving at the time of the survey, approximately one third were reported to have had at least one form of unsafe motor vehicle operation in the past 6 months, including 21 patients with motor vehicle accidents. Motor vehicle accidents were associated with use of prescription medications with sedative properties and with lower subjective ratings of the patient's driving ability by the informant.(Arch Intern Med. 1991;151:941-946)

The heterogeneity within vascular dementia has made neuropsychological research in this area difficult to interpret. We studied a subtype of vascular dementia, Binswanger's disease (BD), diagnosed according to recently specified clinical and radiological criteria. Measures of episodic and semantic memory were administered to BD patients, patients with Alzheimer's disease (AD) comparable to the BD sample in dementia severity, age, and education, and normal controls. Episodic memory was more defective in AD than in BD; these patient groups were equally impaired on measures of semantic memory. The findings suggest that assessment of episodic memory may be useful in differentiating AD from BD.

Free recall of word lists was investigated in a sample of 47 patients with dementia of the Alzheimer type (DAT) and 31 normal controls of equivalent age and education. Recall was divided into primary memory (PM) and secondary memory (SM) components based on the number of items intervening between presentation and recall. The findings were as follows: (1) the patients showed a greater deficit on the SM than on the PM measure; (2) there was little evidence of proactive interference in the patient group; (3) the PM and SM measures were independent in the controls but not in the patient group; and, (4) the size of patients' PM deficit increased linearly with increasing items between presentation and attempted recall. These results suggest that the memory disorder of DAT is partially the result of defective PM.

Normal persons show better recognition memory for rare than for common words. In the first experiment, we examined this word frequency effect in 17 patients with dementia of the Alzheimer type (DAT) and 20 normal controls of equivalent age and education. The DAT patients showed a normal tendency to false alarm to common words but failed to show the normal rare word advantage in their hit rate. In a second experiment, we examined normal memory immediately and after a delay of 1 week when it is approximately equivalent to that of DAT patients. There was no attenuation of the usual rare word advantage. These findings suggest that DAT patients fail to encode the featural and intrastructural elements of to-be-remembered verbal information and that this processing deficit may contribute to their impaired recognition memory performance.

Two methods were used to estimate premorbid IQ in a sample of 68 patients with mild dementia: (1) the National Adult Reading Test (NART), a present ability measure, and (2) an age, sex, race, education and occupation regression formula, a demographically based estimate (DIQ). The dementia sample consisted of probable Alzheimer's disease, multi-infarct dementia and a mixture of the two. The sample was divided into three levels of language disturbances (no language disturbance, naming or fluency disturbance, or both naming and fluency disturbance) based upon performance on the Visual Naming test and the Controlled Oral Word Association test. The NART IQ estimates in patients with one or more language disturbances were significantly lower than those in patients without language disturbances despite equivalent DIQ and Mini-Mental Status exam performance. The results suggest that the applicability of the NART to dementia patients with prominent language disturbances is limited.

Two methods for estimating premorbid IQ were employed in a sample of 199 dementia patients and 26 control subjects: (1) the National Adult Reading Test (NART), a present ability measure, and (2) an age, sex, race, education and occupation regression formula-a demographically based estimate. The dementia sample consisted of probable Alzheimer's disease, multi-inf arct dementia and a mixture of the two. Controls consisted of the spouses of the patient sample. The patient sample was divided into three levels of dementia severity equated for age and level of education. The NART estimates in the mild and moderate/severe dementia groups differed significantly from those for the very mildly demented patients and controls. The results suggest that the applicability of the NART in estimating premorbid IQ in dementia may be limited.

We studied 55 cases of cerebellar atrophy identified by computerized tomography. Atrophy was determined by subjective assessment and objective measurements (superior cerebellar cistern, fourth ventricle, and brainstem). Different patterns of cerebellar atrophy were related to clinical diagnoses. A high incidence of vermal atrophy was observed in primary cerebellar degeneration and chronic alcoholism. More than half the patients with alcoholism had hemispheral atrophy. Vermal atrophy and enlargement of superior cerebellar cisterns (but not hemispheral atrophy) were associated with carcinomatous cerebellar degeneration. Atrophy caused by chronic phenytoin usage showed a specific pattern of enlargement of the cisterna magna, cerebellopontine angle, and superior cerebellar cisterns. Supratentorial atrophy was increased significantly only in the alcoholics. In general, limb ataxia, dysarthria, and nystagmus were related to hemispheral but not to vermal atrophy.

We report a case of a 69-year-old woman with an 11-year history of progressive dementia, who was found at autopsy to have classic Pick's disease pathology, as well as extensive paired helical filament-immunoreactive neurities, with few Alzheimer's disease (AD)-like neurofibrillary tangles and no senile plaques. Both Pick bodies and neuritic degeneration were extensive in the neocortex and hippocampal complex. In addition, synaptophysin immunostaining of the hippocampal complex showed a bilaminar pattern of immunoreactivity in the outer molecular layer as previously described in AD.

The pathophysiology and clinical significance of high signal lesions, visualized on magnetic resonance imaging (MRI) in patients with Alzheimer's disease (AD), remain controversial. Since they are known to correlate with vascular disease and vascular risk factors, we reviewed the clinical correlates of periventricular high signal (PVH) and subcortical white matter lesions (WML) in a sample of 106 patients with probable AD, excluding persons with treated vascular risk factors or symptomatic cerebrovascular and cardiovascular disease. Grade 2 PVH were seen in 26 (25%) and scattered WML were identified in 29 (18%). PHV were associated with advancing age and gait disturbance. WML were associated with gait disturbance and incontinence. Neither radiologic finding was related to dementia severity. The findings suggest that these lesions are common in patients with AD even when those with evidence of cerebrovascular disease are excluded; their presence, therefore, should not preclude a diagnosis of AD. Additionally, the data suggest that HSL on MRI may be one of many risk factors associated with functional disability in persons with probable AD.

We examined CTs of patients with senile dementia of the Alzheimer type and age-matched normal controls. Cerebral atrophy was associated with advancing age and the presence, but not the degree, of dementia. CT density numbers in 14 separate brain regions were not related to age or to the presence or degree of dementia. The findings failed to support other reports of decreased CT density in dementia and suggest that the role of CT scan in the evaluation of dementia is limited to ruling out mass lesions.

Seventy-eight hospital patients, 50 years of age or older, were selected for suspected changes in mentation and for the absence of focal or other organic brain disease. They were studied in relation to education, age, cerebral atrophy (by computerized tomography), electroencephalographic (EEG) slowing, and performance in several neuropsychologic tests. Adequate test-retest reliability of the cognitive measures and interjudge reliability of the cerebral atrophy and EEG measures were demonstrated. Stepwise multiple regression analyses suggested the following: (1) EEG slowing is the strongest and most general pathologic influence on cognition in elderly persons without overt brain disease. (2) Cerebral atrophy independently affects primarily the verbal recall of recent and remote information. (3) Age independently affects primarily recent memory for both verbal and nonverbal material. (4) Formal education is a powerful influence that must be accounted for in all studies of the effects of age on cognition.

Neurologic disease may result in a variety of different gait abnormalities. Senile gait is a distinct neurologic disorder and signs of dysfunction of major neuroanatomic systems are absent. The clinical picture is variable. Senile gait is not directly associated with dementing illness and its anatomic basis is unknown. It does not appear related to hydrocephalus. It is a specific clinical entity related to the degeneration of the nervous system. Further studies are needed to better understand this condition and to develop therapeutic approaches.

A 36-year-old woman had the rare combination of congenital hemihypertrophy and ipsilateral congenital indifference to pain. This appears to be the first description of a patient with congenital hemihypertrophy in whom diffuse neurological deficits were found on the involved side.

Computerized tomography was used to measure cerebral ventricular size in hospitalized alcoholic patients, all of whom had evidence of liver disease. Twelve alcoholic patients with neurologic symptoms such as withdrawal seizures, neuropathy, and drug overdose were included. All these patients had normal results from the mental status examinations by the time of discharge. Alcoholic patients had a much higher mean ventricular size compared to 60 control patients. One third of the alcoholics had markedly enlarged ventricles as opposed to only one of the 60 controls.(JAMA 236:365-368, 1976)

We studied the incidence of computed tomography evidence of cerebellar atrophy in 20 elderly patients with dementia, 20 age-matched controls, and 40 younger normal subjects. Cerebellar vermian atrophy was present in 6 of 20 demented patients, 7 of 20 elderly controls, and 1 of 40 younger controls. There was no other atrophy of infratentorial structures except for occasional enlargement of the cisterna magna and cerebellopontine angle cisterns. Vermian atrophy did not correlate with cerebral atrophy (enlargement of either lateral ventricles or cortical sulci). None of these patients had clinical signs of cerebellar dysfunction. Therefore, atrophy of the cerebellar vermis may occur selectively with aging, without atrophy of the cerebral cortex, and without clinical manifestations.

Mental symptoms are common in temporal arteritis. Reported here is a case in which a deficit in nonverbal memory documented with psychological testing resolved after a course of steroids. Besides the global confusional states commonly seen in temporal arteritis, focal intellectual impairment may be seen. It seems possible that some patients presenting with dementia as well as focal mental signs may have temporal arteritis. The diagnosis can easily be made by performing an erythrocyte sedimentation rate and temporal artery biopsy.

TO THE EDITOR. —The Archives recently published two excellent articles1,2 stressing the significance of dementia in patients with multiple sclerosis. In the last 3 years, at the Rush Alzheimer's Disease Center, Chicago, Ill, we have seen three older patients referred to us because of suspected Alzheimer's disease. These three patients (aged 65, 66, and 67 years) all had histories of progressive dementia. In one, mild forgetfulness had been present for as long as 20 years. Two patients had a previous diagnosis of multiple sclerosis, but their general neurologic disability had been mild and had remained stable over many years. Because of this, it was not thought likely by the referring physician that multiple sclerosis could be the cause of the dementia. In the third patient, a diagnosis of multiple sclerosis had never been made. All three patients had abnormalities on physical examination that were consistent with multiple sclerosis (eg

To the Editor.—We had occasion to see a patient who was severely disabled with bilateral foot drop and upper extremity weakness after having received a single dose of vincristine, 2 mg, and other nonneurotoxic medication three weeks earlier. Physical examination was suggestive of a previously inapparent Charcot-Marie-Tooth syndrome.Report of a Case.—The patient was a 60-year-old white man diagnosed as having multiple myeloma in June 1983, who had received 15 cycles of melphalan and prednisone through December 1984, followed by local radiation therapy to the left chest wall and cervical spine. In February 1985, the patient received a single 2-mg dose of vincristine (ready-to-use solution) with 25 mg of doxorubicin and 80 mg of prednisone per day for four days. Approximately six days later, the patient reported increasing fatigue with ambulation, an unsteady gait, and decreased dexterity of the hands with paresthesia and hypesthesia of the distal upper