The Easterbrook Theorem: An Application to Digital Markets

The rise of large firms in the digital economy, including Amazon, Apple, Facebook, and Google, has rekindled the debate about monopolization law. There are proposals to make finding liability easier against alleged digital monopolists by relaxing substantive standards; to flip burdens of proof; and to overturn broad swaths of existing Supreme Court precedent, and even to condemn a law review article. Frank Easterbrook’s seminal 1984 article, The Limits of Antitrust, theorizes that Type I error costs are greater than Type II error costs in the antitrust context, a proposition that has been woven deeply into antitrust law by the Supreme Court. We consider the implications of this assumption on the standard of proof. We find that, taking variants of the Easterbrook assumption as given, the optimal standard of proof is stronger than the preponderance of the evidence standard. Our conclusion is robust to how one specifies the preponderance of the evidence standard and stands in stark contrast to contemporary proposals to reduce or eliminate the burden of proof facing antitrust plaintiffs in digital markets

Improved metabolic control in tetrahydrobiopterin (BH4), responsive phenylketonuria with sapropterin administered in two divided doses vs. a single daily dose

Background: Phenylketonuria (PKU) often requires a lifelong phenylalanine (Phe)-restricted diet. Introduction of 6R-tetrahydrobiopterin (BH4) has made a huge difference in the diets of patients with PKU. BH4 is the co-factor of the enzyme phenylalanine hydroxylase (PAH) and improves PAH activity and, thus, Phe tolerance in the diet. A limited number of published studies suggest a pharmacodynamic profile of BH4 more suitable to be administered in divided daily doses. / Methods: After a 72-h BH4 loading test, sapropterin was initiated in 50 responsive patients. This case-control study was conducted by administering the same daily dose of sapropterin in group 1 (n=24) as a customary single dose or in two divided doses in group 2 (n=26) over 1 year. / Results: Mean daily consumption of Phe increased significantly after the first year of BH4 treatment in group 2 compared to group 1 (p<0.05). At the end of the first year of treatment with BH4, another dramatic difference observed between the two groups was the ability to transition to a Phe-free diet. Eight patients from group 2 and two from group 1 could quit dietary restriction. / Conclusions: When given in two divided daily doses, BH4 was more efficacious than a single daily dose in increasing daily Phe consumption, Phe tolerance and the ability to transition to a Phe-unrestricted diet at the end of the first year of treatment

Twenty-seven mutations with three novel pathologenic variants causing biotinidase deficiency: a report of 203 patients from the southeastern part of Turkey

BACKGROUND: Biotinidase deficiency (BD) is an autosomal recessive inborn error of metabolism characterized by neurologic and cutaneous symptoms and can be detected by newborn screening. Newborn screening for BD was implemented in Turkey at the end of 2008. METHODS: In total, 203 patients who were identified among the infants detected by the newborn screening were later confirmed to have BD through measurement of serum biotinidase activity. We also performed BTD mutation analysis to characterize the genetic profile. RESULTS: Twenty-seven mutations were identified. The most commonly found variants were c.1330G>C (p.D444H), c.1595C>T (p.T532M), c.470G>A (p.R157H), and c.198_104delGCGGCTGinsTCC (p.C33Ffs ) with allele frequencies of 0.387, 0.175, 0.165 and 0.049, respectively. Three novel pathogenic and likely pathogenic variants were identified: p.W140* (c.419G>A), p.S319F (c.956C>T) and p.L69Hfs*24 (c.192_193insCATC). We also identified three mutations reported in just one patient in the past (p.V442Sfs*59 [c.1324delG], p.H447R [c.1340A>G] and p.198delV [c.592_594delGTC]). Although all of the patients were asymptomatic under the treatment of biotin, only one patient, who had the novel c.419G>A homozygous mutation became symptomatic during an episode of acute gastroenteritis with a presentation of ketosis and metabolic acidosis. Among the screened patients, 156 had partial and 47 had profound BD. CONCLUSIONS: We determined the mutation spectra of BD from the southeastern part of Turkey. The results of this study add three more mutations to the total number of mutations described as causing BD

Clinical and molecular findings in 37 Turkish patients with isolated methylmalonic acidemia

BACKGROUND/AIM: Isolated methylmalonic acidemia is caused by complete or partial deficiency of the enzyme methylmalonyl-CoA mutase (mut0 or mut? enzymatic subtype), a defect of its cofactor adenosyl-cobalamin (cblA, cblB, or cblD-MMA) or deficiency of the enzyme methylmalonyl-CoA epimerase. While onset of the disease ranges from the neonatal period to adulthood, most cases present with lethargy, vomiting and ketoacidosis in the early infancy. Major secondary complications are; growth failure, developmental delay, interstitial nephritis with progressive renal failure, basal ganglia injury and cardiomyopathy. We aimed to demonstrate clinical and molecular findings based on long-term follow up in our patient cohort. MATERIALS AND METHODS: The study includes 37 Turkish patients with isolated MMA who were followed up for long term complications 1 to 14 years. All patients were followed up regularly with clinical, biochemical and dietary monitoring to determine long term complications. Next Generation Sequencing technique was used for mutation screening in five disease-causing genes including; MUT, MMAA, MMAB, MMADHC, MCEE genes. Mutation screening identified 30 different types of mutations. RESULTS: While 28 of these mutations were previously reported, one novel MMAA mutation p.H382Pfs*24 (c.1145delA) and one novel MUT mutation IVS3+1G>T(c.752+1G>T) has been reported. The most common clinical complications were growth retardation, renal involvement, mental motor retardation and developmental delay. Furthermore, one of our patients developed cardiomyopathy, another one died because of hepatic failure and one presented with lactic acidosis after linezolid exposure. CONCLUSIONS: We have detected two novel mutations, including one splice-site mutation in the MUT gene and one frame shift mutation in the MMAA gene in 37 Turkish patients. We confirm the genotype-phenotype correlation in the study population according to the long term complications

Quantum bath refrigeration towards absolute zero: unattainability principle challenged

A minimal model of a quantum refrigerator (QR), i.e. a periodically phase-flipped two-level system permanently coupled to a finite-capacity bath (cold bath) and an infinite heat dump (hot bath), is introduced and used to investigate the cooling of the cold bath towards the absolute zero (T=0). Remarkably, the temperature scaling of the cold-bath cooling rate reveals that it does not vanish as T->0 for certain realistic quantized baths, e.g. phonons in strongly disordered media (fractons) or quantized spin-waves in ferromagnets (magnons). This result challenges Nernst's third-law formulation known as the unattainability principle

Clinical features of 27 Turkish Propionic acidemia patients with 12 novel mutations

Propionic acidemia (PA) is an inherited metabolic disease caused by the deficiency of one of the four biotin-dependent enzymes propionyl-CoA carboxylase (PCC), and is characterized by coma and death in unrecognized patients, additionally late diagnosis leads to severe developmental delay and neurological sequels. Manifestations of PA over time can include growth impairment, intellectual disability, seizures, basal ganglia lesions, pancreatitis, and cardiomyopathy. Other rarely reported complications include optic atrophy, hearing loss, premature ovarian insufficiency, and chronic renal failure. Mutations in PCCA-PCCB genes cause the clinically heterogeneous disease of PA. In this study, we investigate the mutation spectrum of PCCAPCCB genes and phenotypic features of 27 Turkish patients with PA from the South and Southeast parts of Turkey. We report 12 novel PA mutations, five affecting the PCCA gene and 7 affecting the PCCB gene

The outcome of 41 Late-Diagnosed Turkish GA-1 Patients: A Candidate for the Turkish NBS

Background: Glutaric aciduria type 1(GA-1) is an inherited cerebral organic aciduria. Untreated patients with GA-1 have a risk of acute encephalopathic crises during the first 6 years of life. In so far as GA-1 desperately does not exist in Turkish newborn screening (NBS) program, most patients in our study were late-diagnosed. / Method: This study included 41 patients diagnosed with acylcarnitine profile, urinary organic acids, mutation analyses in the symptomatic period. We presented with clinical, neuroradiological, and molecular data of our 41 patients. / Results: The mean age at diagnosis was 14.8 13.9 (15 days to 72 months) and, high blood glutaconic acid, glutarylcarnitine and urinary glutaric acid (GA) levels in 41 patients were revealed. Seventeen different mutations in the glutaryl-CoA dehydrogenase gene were identified, five of which were novel. The patients, most of whom were late-diagnosed, had a poor neurological outcome. Treatment strategies made a little improvement in dystonia and the frequency of encephalopathic attacks. / Conclusion: All GA-1 patients in our study were severely affected since they were latediagnosed, while others show that GA-1 is a treatable metabolic disorder if it is diagnosed with NBS. This study provides an essential perspective of the severe impact on GA-1 patients unless it is diagnosed with NBS. We immediately advocate GA-1 to be included in the Turkish NBS

Mucopolysaccharidosis Type-II with Pathognomonic Skin Appearance: A Case with Pebbling Sign

Mucopolysaccharidosis type-II (MPS-II) is an X-linked lysosomal storage disorder. Here, we report an 8-year-old boy with pebbling sign in the scapular region, coarse facies, claw hand, diastolic murmur, and hepatomegaly. With decreased iduronate-2-sulfatase activity and hemizygous mutation in the IDS gene, the diagnosis was MPS-II. Pebbling sign is a rare but pathognomonic sign of MPS-II

Dynamics of Three Agent Games

We study the dynamics and resulting score distribution of three-agent games where after each competition a single agent wins and scores a point. A single competition is described by a triplet of numbers $p$, $t$ and $q$ denoting the probabilities that the team with the highest, middle or lowest accumulated score wins. We study the full family of solutions in the regime, where the number of agents and competitions is large, which can be regarded as a hydrodynamic limit. Depending on the parameter values $(p,q,t)$, we find six qualitatively different asymptotic score distributions and we also provide a qualitative understanding of these results. We checked our analytical results against numerical simulations of the microscopic model and find these to be in excellent agreement. The three agent game can be regarded as a social model where a player can be favored or disfavored for advancement, based on his/her accumulated score. It is also possible to decide the outcome of a three agent game through a mini tournament of two-a gent competitions among the participating players and it turns out that the resulting possible score distributions are a subset of those obtained for the general three agent-games. We discuss how one can add a steady and democratic decline rate to the model and present a simple geometric construction that allows one to write down the corresponding score evolution equations for $n$-agent games

Analytical Solution of a Stochastic Content Based Network Model

We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches, for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behavior to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show scaling behavior. The results might be of interest for understanding the emergence of genomic interaction networks, which rely, to a large extent, on mechanisms based on sequence matching, and exhibit similar global features to those found here.Comment: 13 pages, 5 figures. Rewrote conclusions regarding the relevance to gene regulation networks, fixed minor errors and replaced fig. 4. Main body of paper (model and calculations) remains unchanged. Submitted for publicatio