The Effects of a Stellar Encounter on a Planetesimal Disk

We investigate the effects of a passing stellar encounter on a planetesimal disk through analytical calculations and numerical simulations, and derive the boundary radius ($a_{\rm planet}$) outside which planet formation is inhibited by disruptive collisions with high relative velocities.Comment: 25 pages, 11 figures, included in 15 tex-files, 7 ps-files and 4 eps-file

Rapid Formation of Saturn after Jupiter Completion

We have investigated Saturn's core formation at a radial pressure maximum in a protoplanetary disk, which is created by gap opening by Jupiter. A core formed via planetesimal accretion induces the fragmentation of surrounding planetesimals, which generally inhibits further growth of the core by removal of the resulting fragments due to radial drift caused by gas drag. However, the emergence of the pressure maximum halts the drift of the fragments, while their orbital eccentricities and inclinations are efficiently damped by gas drag. As a result, the core of Saturn rapidly grows via accretion of the fragments near the pressure maximum. We have found that in the minimum-mass solar nebula, kilometer sized planetesimals can produce a core exceeding 10 Earth masses within two million years. Since Jupiter may not have undergone significant type II inward migration, it is likely that Jupiter's formation was completed when the local disk mass has already decayed to a value comparable to or less than Jovian mass. The expected rapid growth of Saturn's core on a timescale comparable to or shorter than observationally inferred disk lifetime enables Saturn to acquire the current amount of envelope gas before the disk gas is completely depleted. The high heat energy release rate onto the core surface due to the rapid accretion of the fragments delays onset of runaway gas accretion until the core mass becomes somewhat larger than that of Jupiter, which is consistent with the estimate based on interior modeling. Therefore, the rapid formation of Saturn induced by gap opening of Jupiter can account for the formation of multiple gas giants (Jupiter and Saturn) without significant inward migration and larger core mass of Saturn than that of Jupiter.Comment: Accepted for publication in Ap

Planetary Core Formation with Collisional Fragmentation and Atmosphere to Form Gas Giant Planets

Massive planetary cores ($\sim 10$ Earth masses) trigger rapid gas accretion to form gas giant planets \rev{such as} Jupiter and Saturn. We investigate the core growth and the possibilities for cores to reach such a critical core mass. At the late stage, planetary cores grow through collisions with small planetesimals. Collisional fragmentation of planetesimals, which is induced by gravitational interaction with planetary cores, reduces the amount of planetesimals surrounding them, and thus the final core masses. Starting from small planetesimals that the fragmentation rapidly removes, less massive cores are formed. However, planetary cores acquire atmospheres that enlarge their collisional cross section before rapid gas accretion. Once planetary cores exceed about Mars mass, atmospheres significantly accelerate the growth of cores. We show that, taking into account the effects of fragmentation and atmosphere, initially large planetesimals enable formation of sufficiently massive cores. On the other hand, because the growth of cores is slow for large planetesimals, a massive disk is necessary for cores to grow enough within a disk lifetime. If the disk with 100\,km-sized initial planetesimals is 10 times as massive as the minimum mass solar nebula, planetary cores can exceed 10 Earth masses in the Jovian planet region ($>5\,$AU).Comment: accepted for publication in Ap

Smoothness Analysis of Adversarial Training

Deep neural networks are vulnerable to adversarial attacks. Recent studies about adversarial robustness focus on the loss landscape in the parameter space since it is related to optimization and generalization performance. These studies conclude that the difficulty of adversarial training is caused by the non-smoothness of the loss function: i.e., its gradient is not Lipschitz continuous. However, this analysis ignores the dependence of adversarial attacks on model parameters. Since adversarial attacks are optimized for models, they should depend on the parameters. Considering this dependence, we analyze the smoothness of the loss function of adversarial training using the optimal attacks for the model parameter in more detail. We reveal that the constraint of adversarial attacks is one cause of the non-smoothness and that the smoothness depends on the types of the constraints. Specifically, the $L_\infty$ constraint can cause non-smoothness more than the $L_2$ constraint. Moreover, our analysis implies that if we flatten the loss function with respect to input data, the Lipschitz constant of the gradient of adversarial loss tends to increase. To address the non-smoothness, we show that EntropySGD smoothens the non-smooth loss and improves the performance of adversarial training.Comment: 22 pages, 7 figures. In V3, we add the results of EntropySGD for adversarial trainin

ラッテの血清成分の濃度に対するGoitrogenの効果

The research was carried out to study the serum concentrations of blood components in the hypothyroidism, using the Wister strain rats. As a goitrogen, methylthiouracil (methiocil; 6-methy I -2-thiouracil) was used. The compound was suspended in 2% of aqueous sol of carboxymethyl cellulose and the suspension was injected into the stomach or injected subcutaneously. In one experiment, the goitrogen disolved partially in aqueous solution of sodium hydroxide was injected subcutaneously to the rats. The period of administration was 12 hours (4 times of injection, 3 hours interval) or of approximately one week, twice injection a day. The blood was taken at 3 hours following the final administration, and serum of the blood was determined for total protein(TP), albumin(Alb), globulin(Gl), glucose(Glu), blood ureal nitrogen(BUN), cholesterol(Chol), Calcium(Ca), magnesium(Mg), and phosphorus(P). By the administration of the goitrogen, serum concentrations of BUN, Chol, Mg increased and that of P decreased. Ratio of Alb/Gl in the serum concentration also was high in the group treated with methiocil in comparison with the control group. Oral treatment of methiocil increased only glycine among amino acids in the serum. The changes of concentration of blood serum component following the administration of goitrogen indicates that steer producing the beef with high degree of fat deposit is in a state of hypothyroidism

肥育牛の肉質と血液成分の関係について

In fattened steers of Holstein breed correlation coefficients between factors of the carcass, and between roast grade and size of selected body parts were studied. Study of correlation between roast grade and levels of serumal components of blood taken at slaughter was carried out in the steer above mentioned. Roast grade had minus significant correlation to fat cover depth and daily gain, and plus significant correlation to hips width and thurls width. Correlations between roast grade and concentration of blood serum magnesium or cholesterol were shown, but not significant. There were significant minus correlations between roast grade and concentrations of TP, Al, Gl, Ca, Ca/Mg in the serum. Ratio of Mg/ (Ca+P+Mg) had a significant positive correlation to roast grade. When grouped by sire, steers group with low daily gain had generally a high quality of roast

ラッテの血清の成分およびアミノ酸粗成に対するグルココルチコイドの効果

For induction of fat deposit in meat, hypothyroidism is the most important factor. This study was carried out to confirm the effect of glucocorticoid on thyroidal function, using rats. Triamcinolone acetonid, a synthetic compound was used as glucocorticoid. Rats of an experimental group were injected singly subcutaneously with 0.9 mg of the compound and another group of rats served as control. The animals were sacrificed by decapitating at 2 hours and 4 hours following the injection. At the time of decapitating, blood was obtained from the animal respectively. A half portion of the blood serum was used for determination of such blood components as total protein (TP), albumin (Alb), globulin (Gl), blood ureal nitrogen (BUN), glucose(Glu), cholesterol (Chol), calcium (Ca), magnesium (Mg) and phosphorus (P). Another half portion of the serum was subjected to amino acid analysis, using a automatic amino acid analyzer. By injection of the glucocorticoid, concentrations of TP, Alb, and Gl decreased, and concentration of amino acids increased. This is due to gluconeogenesis induced by glucocorticoid. Serum phosphorus was elevated, and ratio of Ca/P decreased and P/Mg increased. These are indicative of lowered thyroidal function. Accordingly, glucocorticoid seemed to have a favourable effect on fattening cattle. Results of amino acid assay were summarized in Table 2. Most of amino acids increased by the injection of the compound, except glutamic acid and taurine. This is due to protein catabolism and gluconeogenesis. Concentration of serum glucose consistently increased. Increase of glycine concentration in serum is indicative of hyperthyroidism. This is, however, due to neoglucogenesis by cortisol. Low concentration of Mg is indicative of hyperthyroidism. Further study for the effect of glucocorticoid would be required, since glucocorticoid is considered to accelerate production of lean meat

Switching One-Versus-the-Rest Loss to Increase the Margin of Logits for Adversarial Robustness

Adversarial training is a promising method to improve the robustness against adversarial attacks. To enhance its performance, recent methods impose high weights on the cross-entropy loss for important data points near the decision boundary. However, these importance-aware methods are vulnerable to sophisticated attacks, e.g., Auto-Attack. In this paper, we experimentally investigate the cause of their vulnerability via margins between logits for the true label and the other labels because they should be large enough to prevent the largest logit from being flipped by the attacks. Our experiments reveal that the histogram of the logit margins of na\"ive adversarial training has two peaks. Thus, the levels of difficulty in increasing logit margins are roughly divided into two: difficult samples (small logit margins) and easy samples (large logit margins). On the other hand, only one peak near zero appears in the histogram of importance-aware methods, i.e., they reduce the logit margins of easy samples. To increase logit margins of difficult samples without reducing those of easy samples, we propose switching one-versus-the-rest loss (SOVR), which switches from cross-entropy to one-versus-the-rest loss (OVR) for difficult samples. We derive trajectories of logit margins for a simple problem and prove that OVR increases logit margins two times larger than the weighted cross-entropy loss. Thus, SOVR increases logit margins of difficult samples, unlike existing methods. We experimentally show that SOVR achieves better robustness against Auto-Attack than importance-aware methods.Comment: 25 pages, 18 figure

血清の成分及びアミノ酸の濃度に対するビタミンの効果

Effects of different vitamins on concentration of blood serum components and amino acid were studied, using male rats of the Wister strain. Five kinds of vitamins, namely vitamin A, v. B1 (thiamin), v. C (ascorbic acid), v. D (calciferol), v. E (tocopherol) were used in this study. They were injected sub cutaneously in a single dose of 500 IU, 2.5 mg, 2.5 mg, 1000 IU and 2.5 mg, respectively. The animals were sacrificed by decapitating at four hours following the injection. Blood sample taken at the time of sacrifice was centrifuged for separation of serum after 10 hours-standing at room temperature. The serum was determined for concentration of its components, using Vet-Aid described previously and analyzed for amino acids, using a full automatic amino acid analyzer previously described. Concentration of cholesterol in the serum was elevated by the administration of vitamins A, B and C, and it was lowered significantly by the administration of vitamins D and E. These vitamins seemed to have a close relation to fat deposition in the meat. The effect of vitamins on fat deposition in beef would require further study