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Atlantic cod Gadus morhua has polymorphic haemoglobin, which can be separated into two homozygous types, HbI-1 and HbI-2, and one heterozygous type HbI-1/2. The geographical distribution of Atlantic cod with the different haemoglobin types varies, with the HbI2 allele occurring at high frequency in northern regions, and the HbI1 allele dominant in warmer areas. To determine if temperature is a selective parameter in the distribution of the haemoglobin types, the preferred temperature of the homozygous genotypes HbI-1 and HbI-2 was measured. We found that HbI-2 cod preferred a temperature of 8.2±1.5°C while HbI-1 cod preferred 15.4±1.1°C, and this preference was significant. The effect of hypoxia (35% oxygen saturation) on the preferred temperature was also measured. Previous studies showed that the preferred temperature of fish decreases during hypoxia, and this was the case for HbI-1 cod, which preferred 9.8±1.8°C during hypoxia, whereas HbI-2 cod did not show this effect. The results indicate that environmental temperature changes will lead to a distributional change in the different haemoglobin types of Atlantic cod,global warming providing an advantage for HbI-1 cod. However, since HbI-1 cod prefer a low temperature under hypoxic conditions, a combination of increased water temperature and hypoxia could be unfavourable for Atlantic cod stocks.

The different types of Atlantic cod haemoglobin have been known since 1961(Sick, 1961). Experiments with agar gel electrophoresis revealed that Atlantic cod haemoglobin consists of two homozygous genotypes (HbI-1 and HbI-2) and one heterozygous genotype(HbI-1/2). These genotypes are controlled by two alleles, referred to as HbI1 and HbI2. Such polymorphism of fish haemoglobin is prevalent (Kirpichnikov, 1981)and is often essential if fish change habitat during their development(ontogenetic effect), or if they shift between different environments where changes in respiration media, salinity etc. can occur(Jensen et al., 1998). In some cases, however, the reason why some fish, such as Atlantic cod, have more than one haemoglobin type is unknown.

When searching for the reason why Atlantic cod have polymorphic haemoglobin we examined the frequency distribution of the two alleles coding for the different haemoglobin types. The distribution is extremely heterogeneous across the North Atlantic. The HbI2 allele reaches up to 99%frequency in Greenland waters and is also dominant in northern Norway,Iceland, the Faeroe Islands, Canada and in the northern part of the Baltic,whereas the HbI1 allele is dominant in the warmer areas (Sick, 1965a, b; Frydenberg et al., 1965). The difference between the homozygous genotypes is limited to an extra histidine-containing peptide in the HbI-1 type, and therefore the structural differences are only minimal (Rattazzi and Pik, 1965). However, differences in biochemical properties have been described for the genotypes. The oxygen affinity of haemoglobin is higher for HbI-2 cod at low temperatures (<10°C)(Karpov and Novikov, 1981; Brix et al., 1998; McFarland, 1998), and for HbI-1 cod, at some blood pH values, at high temperatures (>14°C)(Karpov and Novikov, 1981; Brix et al., 1998). The heterozygous haemoglobin type is generally found to have oxygen affinity values that are intermediate to HbI-1 and HbI-2(Karpov and Novikov, 1981). This information suggests that temperature could be a selective parameter for the distribution of Atlantic cod with different haemoglobin types. The present study examined whether this was the case by measuring the preferred temperature of HbI-1 and HbI-2 cod.

The preferred temperature of a species is not a fixed value because it can be influenced by other parameters. Seasonal fluctuation of the preferred temperature is highest during summertime and lowest during winter(Clark and Green, 1991). The amount of food consumed by the fish also changes their preferred temperature. Fish fed with the lowest food ration prefer the lowest temperature(Despatie et al., 2001). In addition, hypoxia results in a decrease of the preferred temperature(Schurmann et al., 1991; Schurmann and Steffensen,1992). Since hypoxia is a common phenomenon in several habitats where the Atlantic cod is represented, especially in coastal regions such as the Gulf of St Lawrence (Chabot and Dutil,1999) and the Baltic Sea(Nielsen and Gargas, 1984), we analysed the effect of hypoxia on the preferred temperature for the different haemoglobin types.

### Experimental animals

Juvenile Atlantic cod Gadus morhua L. were caught by trawl in the northern part of Øresund (Denmark) during the summer months. They were kept under a 16h:8h light:dark cycle at 10°C in aerated water tanks (500 litre) that were continuously supplied with recirculating filtered 30‰seawater (8l min-1). The cod were fed regularly with chopped herring Clupea harengus, and were in good condition. Several months prior to the experiments they were pit-tagged and their haemoglobin type analysed (as described below). Cod with haemoglobin types HbI-1 and HbI-2 were pre-selected for the preferred temperature experiments.

### Determination of haemoglobin genotype

The haemoglobin genotypes were determined by agar gel electrophoresis(Fyhn et al., 1994). 0.2ml of blood was sampled from the caudal vein with a heparinized syringe. The blood sample was centrifuged at 3000g in an Eppendorf tube and the plasma discarded. 50 μl of the red blood cells (RBC) were transferred to a new Eppendorf tube and washed twice with 60 μl of 1.17% NaCl solution. 80μl of cold distilled water was added to haemolyse the RBC. The sample was refrigerated for 10 min, and subsequently centrifuged for 5 min at 3000 g. To ensure proper sinking in the gel, 40 μl of haemolysed RBC (supernatant) was mixed with 35 μl of 40% sucrose solution. A gel was prepared using 1% agar (Difco bactoagar) dissolved by warming in Smithies buffer (pH 8.6) diluted 1:1 with distilled water. Diluted Smithies buffer was also used as electrophoresis buffer. All samples were electrophoresed at a 40 mA current for 35 min at 10°C, using a Pharmacia EPS600 power supply.

### Shuttle box technique

To determine the preferred temperature, cod of body mass 90-200 g were allowed to thermoregulate in an electronic shuttle box. The shuttle box consisted of a warm and a cold water chamber connected by a tube. The fish was able to thermoregulate by shuttling between the two chambers. The temperature difference between the two chambers was 2°C and was kept constant by the use of two pumps (Eheim 1046). When the fish occupied the cold chamber the entire system was cooled down (4°Ch-1), whereas the system started heating up when the fish entered the warm chamber(4°Ch-1). The position of the fish was registered by a CCD camera connected to a PC video frame-grabber (Visionetics VFG-512 BC),digitising at 25 frames s-1, at a resolution of 256×256 pixels. Three 40 W red light bulbs illuminated the shuttle box from below and made the fish look like a black silhouette on a light background. The contrast between the fish and its surroundings was used by a custom-designed software program to detect the geometric centre of the silhouette of the fish. The x,y coordinates of the position of the fish were transmitted via an RS-232 port to a second computer. The second computer was equipped with Labtech Notebook programmed to switching on either cooling or heating, depending on the position of the fish (for further details, see Schurmann et al., 1991;Schurmann and Steffensen, 1992, 1994).

The oxygen saturation was measured by a microprocessor oximeter (WTW oxy 96) in the warm part of the shuttle box. Test measurements showed that the difference in oxygen saturation between the two chambers never exceeded 2%. The oxygen saturation could be regulated via a computer system equipped with Labtech Notebook, which controlled solenoid valves. When the oxygen saturation was above the selected set point (35% oxygen saturation)compressed nitrogen was added to the system.

### Experimental protocol

The cod was introduced to the shuttle box 24 h prior to the experiment at a water temperature of 10°C. The experiments were carried out during daytime, where the highest activity and the most precise thermoregulation of the cod were previously observed. The data collection period consisted of 4 h of normoxia (>80% oxygen saturation) followed by a 2 h reduction in oxygen saturation, again followed by 3 h of hypoxia (35% oxygen saturation).

### Calculations and analysis

To estimate the body temperature of a fish in a shuttle box system Newton's Law of Cooling may be used:
$\ T_{\mathrm{b}}=T_{\mathrm{a}}+(T_{\mathrm{i}}-T_{\mathrm{a}})e^{-\mathrm{kt}},$
1
where Tb is body temperature, Ta is ambient temperature, Ti is the initial body temperature, t is time (min) and k is the rate of change of the core temperature (min-1). Stevens and Sutterlin(1976) previously measured the value of k for another temperate saltwater fish, the sea raven(Hemitripterus americanus), and found it to be related to the body mass (W), measured in g:
$\ k=3.32{\times}W^{-0.536}.$
2
We chose this value of k to calculate the body temperature of Atlantic cod, since it is the most relevant literature value. The preferred temperature of each fish was calculated as the median of the estimated body temperature. Swimming speed was calculated as body lengths(BL)s-1 and measured as the distance in pixels(corresponding to a known distance in cm) swum s-1.

Analyses of variance (ANOVA) tested the effects of the independent factors(HbI-genotype and oxygen saturation) and their interactions on the preferred temperature or swimming speed. The Student Newman—Keul method was used in cases where the two-way ANOVA showed a significant difference(P<0.05).

The preferred temperature was calculated as the median preferred temperatures ± S.D. of eight fish during normoxia (>80% oxygen saturation) and eight fish during hypoxia (35% oxygen saturation). The experiment was done for both HbI-1 and HbI-2 cod(Table 1). During normoxic conditions HbI-1 cod preferred a significantly higher (P<0.0001)temperature (15.4±1.1°C) compared with HbI-2 cod(8.2±1.5°C). When exposed to hypoxia, however, no difference was observed between the two genotypes. This was as a result of HbI-1 cod decreasing the preferred temperature significantly (P<0.0005)(9.8±1.8°C), while the preferred temperature of HbI-2 cod was relatively unchanged (8.0±2.9°C). The upper and lower avoidance temperatures indicate that the cod are precise thermoregulators. The avoidance temperatures are calculated as the median of the highest or lowest temperatures experienced by the fish and show that the fish shuttles within a narrow range of temperatures. Despite the difference in preferred temperature between the two haemoglobin types at normoxia, the swimming speed did not differ significantly (0.38±0.05 and 0.29±0.09 BLs-1). However, both haemoglobin types decreased their swimming speeds significantly (P<0.0001) when facing hypoxia and reached a similar level of 0.16±0.08 and 0.17±0.08 BLs-1. Changes in preferred temperature and swimming speed for the two haemoglobin types, as described above, are illustrated in Fig. 1, which includes an experimental period where the fish is exposed to normoxia and hypoxia.

Table 1.

Preferred temperature, lower and upper avoidance temperatures and swimming speed of Atlantic cod with different haemoglobin genotypes

NPreferred temperature (°C)Lower avoidance temperature (°C)Upper avoidance temperature (°C)Swimming speed (BLs-1)
HbI-1 15.4±1.1 14.0±0.9 16.0±0.8 0.38±0.05
>80% O2 saturation
HbI-2 8.2±1.5 7.2±1.6 9.3±1.6 0.29±0.09
>80% O2 saturation
HbI-1 9.8±1.8 9.3±1.8 11.2±2.2 0.17±0.08
35% O2 saturation
HbI-2 8.0±2.9 7.3±2.8 9.5±2.9 0.16±0.08
35% O2 saturation
NPreferred temperature (°C)Lower avoidance temperature (°C)Upper avoidance temperature (°C)Swimming speed (BLs-1)
HbI-1 15.4±1.1 14.0±0.9 16.0±0.8 0.38±0.05
>80% O2 saturation
HbI-2 8.2±1.5 7.2±1.6 9.3±1.6 0.29±0.09
>80% O2 saturation
HbI-1 9.8±1.8 9.3±1.8 11.2±2.2 0.17±0.08
35% O2 saturation
HbI-2 8.0±2.9 7.3±2.8 9.5±2.9 0.16±0.08
35% O2 saturation

Values are means of medians ± S.D. (temperature values only).

The preferred temperature was significantly different (P=0.0001)between HbI-1 and HbI-2 at normoxia and between HbI-1 at normoxia compared with HbI-1 at hypoxia (P=0.0005).

Swimming speed decreased significantly (P=0.0001) for both haemoglobin types when exposed to hypoxia.

Fig. 1.

Oxygen saturation, swimming speed and water temperature measured for cod with haemoglobin type HbI-1 and HbI-2. When the oxygen saturation is lowered to 35% the preferred temperature of HbI-1 cod decreases, while this tendency is absent for HbI-2 cod. For both the haemoglobin types the swimming speed decreases during hypoxia. Measurements were made every second and each point is a mean value calculated for 1 h.

Fig. 1.

Oxygen saturation, swimming speed and water temperature measured for cod with haemoglobin type HbI-1 and HbI-2. When the oxygen saturation is lowered to 35% the preferred temperature of HbI-1 cod decreases, while this tendency is absent for HbI-2 cod. For both the haemoglobin types the swimming speed decreases during hypoxia. Measurements were made every second and each point is a mean value calculated for 1 h.

A highly significant difference was found between the preferred temperatures of HbI-1 and HbI-2 cod. The temperature preferred by HbI-1 cod(15.4±1.1°C) compared to HbI-2 cod (8.2±1.5°C) proves that temperature is a selective parameter in the heterogeneous distribution of the haemoglobin types. This conclusion is illustrated in Fig. 2, which shows the frequency of the HbI1 allele throughout the Atlantic cod's range,plotted on a sea surface temperature map. Schurmann and Steffensen(1992) previously examined the preferred temperature of juvenile cod captured near Helsingør in Denmark. They found a preference for 13.9±2.7°C without taking different haemoglobin types into consideration. Sick(1965a) found the distribution of HbI-1, HbI-1/2 and HbI-2 in this area to be 31%, 51% and 18%, respectively. While the preferred temperature of HbI-1/2 is not known, the result of Schurmann and Steffensen(1992) indicates that it may be situated somewhere between those of HbI-1 and HbI-2. Clark and Green(1991) and Despatie et al.(2001) also measured the preferred temperature of Atlantic cod in Canada, where the HbI2allele is dominating, and in both studies the preferred temperature was lower than 10°C.

Fig. 2.

Sea surface temperatures (spring) and the frequency distribution of the HbI1 allele throughout the range of the Atlantic cod (Sick, 1965a,b; Frydenberg et al., 1965). The frequency of the HbI1 allele is low in cold water regions and become more dominant in warmer areas. A clear cline is found along the Norwegian coast.

Fig. 2.

Sea surface temperatures (spring) and the frequency distribution of the HbI1 allele throughout the range of the Atlantic cod (Sick, 1965a,b; Frydenberg et al., 1965). The frequency of the HbI1 allele is low in cold water regions and become more dominant in warmer areas. A clear cline is found along the Norwegian coast.

Periods of hypoxia occur in coastal areas, and in the late summer months the oxygen saturation can be as low as 20-40% in Danish waters(Nielsen and Gargas, 1984). In the present study an oxygen saturation of 35% resulted in a significant decrease in the preferred temperature for cod with HbI-1 genotype from 15.4±1.1 to 9.8±1.8°C. There are several physiological advantages in lowering the body temperature during hypoxia, including lower metabolic rate, higher oxygen affinity for haemoglobin and higher oxygen solubility in the water (Jobling,1994). The disadvantages of preferring lower water temperatures during hypoxia are a reduction in swimming speed as well as a reduction in food intake and digestion rate, which results in decreased growth(Brett, 1971). Changes in enzyme conformation, membrane structure and acid—base regulation are also consequences of a sudden decrease in temperature(Reynolds and Casterlin, 1980; Jobling, 1994). A decrease in the preferred temperature as a consequence of hypoxia has both advantages and disadvantages for the fish. Hypoxia, however, seems to be nothing but a disadvantage for the fish. Chabot and Dutil(1999) found that the growth rate of Atlantic cod at 10°C decreased significantly when the oxygen fell below 56% saturation. In the same study it was observed that spontaneous activity also decreases during hypoxia.

The observation that the preferred temperature of HbI-2 cod did not decrease as a consequence of hypoxia (8.2±1.5-8.0±2.9°C)indicates that the energy saving advantages of an even lower temperature was not necessary for the cod to survive. This conclusion makes sense, since the preferred temperature of HbI-1 cod never went below this temperature during hypoxia. Schurmann and Steffensen(1992) found that the lowest preferred temperature correlated with the lowest oxygen saturation (15%). If the HbI-2 genotypes had been exposed to the same low level of hypoxia,possibly the preferred temperature would have been significantly lower.

In the present study swimming speeds for HbI-1 and HbI-2 cod at normoxia were 0.38 and 0.29 BL s-1, respectively. These swimming speeds correspond with values obtained in previous studies(Schurmann and Steffensen,1994). Whether the haemoglobin type actually affects the swimming speed is not known, but since the preferred temperature is thought to be the zone where physiological processes are optimised or maximized(Jobling, 1994), the question is relevant.

Hypoxia (35% oxygen saturation) significantly lowered the swimming speed for both haemoglobin types (0.17 and 0.16 BL s-1). The preferred temperature also decreased for HbI-1 exposed to hypoxia. Since Schurmann and Steffensen(1994) found a tendency of a higher swimming speed at 10°C compared to 15°C, the decrease in swimming speed for HbI-1 cod in the present study was probably caused by hypoxia and not by the temperature. The levels of swimming speed at 35% oxygen saturation correspond to previous measurement for Atlantic cod; 0.18 BL s-1 was the average swimming speed at 30% oxygen saturation measured at 5°C and 10°C by Schurmann and Steffensen(1994). The reduction in swimming speed during hypoxia will not only decrease the oxygen requirement of the Atlantic cod, but also reduce the chance of reaching a more favourable environment. Another strategy for fish during hypoxia is to increase the activity level, which enhances the probability of encountering better oxygen conditions. The latter strategy is observed for the skipjack tuna(Katsuwonus pelamis) (Dizon,1977) and the red hake (Urophycis chuss)(Bejda et al., 1987).

The consequence of the difference in the preferred temperature of HbI-1 and HbI-2 cod should be a differentiation of physiological processes(Jobling, 1994). So far only a limited number of studies have distinguished between the haemoglobin types when studying physiology and behaviour of Atlantic cod. An exeption was McFarland (1998) who differentiated between the haemoglobin types when measuring the metabolism,and found that HbI-2 cod had a significantly lower standard metabolic rate at 4°C compared with HbI-1 cod. Feeding behaviour has also been examined and the result showed that the competitive performance was highest for HbI-2 cod measured at 6°C (Salvanes and Hart,2000). The advantageous feeding behaviour for HbI-2 cod at low water temperatures is also reflected in growth-related parameters; HbI-2 cod from mid to northerly Norwegian coastal waters has a higher growth rate and earlier age of first spawning than HbI-1 cod(Jørstad and Nævdal,1994; Mork et al., 1983, 1984). It seems that the theory of optimised physiological performances at the preferred temperature fits HbI-2 cod perfectly, whereas the advantages of HbI-1 cod at high water temperatures are more blurred and less well known. We predict that there are more physiological and behavioural differentiations between the haemoglobin types due to their different preferred temperatures. These results suggest that for physiological and behavioural studies as well as for aquacultural use, Atlantic cod should be subdivided according to its haemoglobin type.

The coupling between temperature and the occurrence of cod with different haemoglobin genotypes is of interest when discussing the biological consequences of increased water temperatures due to global warming. The results from the present study indicate that increasing water temperatures will result in an increased frequency of HbI-1 cod, because this haemoglobin type prefers a higher temperature. Furthermore, Atlantic cod stocks will move north if the seawater temperature exceeds the preferred temperature of the HbI-1 genotype. If a combination of increased water temperature and hypoxia should occur, the predicted superiority of HbI-1 cod as a consequence of increased water temperatures, and the fact that HbI-1 cod prefers a lower temperature during hypoxia, will cause an unfavourable situation for the HbI-1 cod. This situation is especially relevant in coastal regions where hypoxia is common, and could cause extensive damage to the Baltic cod stock, for example.

We thank Professor E. W. Taylor and Dr S. McFarland (University of Birmingham) for inspiration and Ferret for the graphics in this paper(www.ferret.noaa.gov). Financial support was provided by the Carlsberg Foundation, Danish Natural Sciences Research Council, NARP (Nordic Arctic Research Program), and the E.& K. Petersen Foundation.

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# If the length of a 46 cm spring increases to 77 cm when a 16 kg weight is hanging from it, what is the spring's constant?

Hooke's Law can be rearranged as $k = \frac{F}{x}$. In this case $F$ is the weight force, $m g = 16 \cdot 9.8 = 156.8$ $N$. The displacement, $x$ is $0.77 - 0.46 = 0.31$ $m$. So $k = \frac{156.8}{0.31} = 505.8$ $N k {g}^{-} 1$ (or $k {g}^{s} - 2$).
Not much more explanation needed, except to note that it was necessary to convert from $c m$ to $m$, the correct SI unit for length and distance.
The units of the spring constant can be expressed as $N k {g}^{-} 1$ or as $k g {s}^{-} 2$.

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• ### Density Functional plus Dynamical Mean-Field Theory of the Spin-Crossover Molecule Fe(phen)$_2$(NCS)$_2$(1503.03547)

We study the spin-crossover molecule Fe(phen)$_2$(NCS)$_2$ using density functional theory (DFT) plus dynamical mean-field theory, which allows access to observables not attainable with traditional quantum chemical or electronic structure methods. The temperature dependent magnetic susceptibility, electron addition and removal spectra, and total energies are calculated and compared to experiment. We demonstrate that the proper quantitative energy difference between the high-spin and low-spin state, as well as reasonably accurate values of the magnetic susceptibility can be obtained when using realistic interaction parameters. Comparisons to DFT and DFT+U calculations demonstrate that dynamical correlations are critical to the energetics of the low-spin state. Additionally, we elucidate the differences between DFT+U and spin density functional theory (SDFT) plus U methodologies, demonstrating that DFT+U can recover SDFT+U results for an appropriately chosen on-site exchange interaction.
• ### Origin of Spinel Nanocheckerboards via First Principles(1501.03480)

Self-organizing nanocheckerboards have been experimentally fabricated in Mn-based spinels, but have not yet been explained with first principles. Using density-functional-theory, we explain the phase diagram of the $\mathrm{ZnMn_xGa_{2-x}O_4}$ system and the origin of nanocheckerboards. We predict total phase separation at zero temperature, then show the combination of kinetics, thermodynamics, and Jahn-Teller physics that generates the system's observed behavior. We find the {011} surfaces are strongly-preferred energetically, which mandates checkerboard ordering by purely geometrical considerations.


text: 3 Further formatting fixes. Please be more thorough when editing posts for formatting - this should only happen once. edited May 18 '15 at 18:01 Emilio Pisanty 90.4k2323 gold badges228228 silver badges466466 bronze badges If we assume potential at infinity to be zero and earthEarth to be spherical then the potential at the surface of the earth is given by $$\frac{kq}{r}$$,$${kq}/{r}$$,where where $$k$$ is a constant  ,  $$q$$ is the charge on earth and $$r$$ its radius.As As $$q$$ is extremely small and $$r$$ very large, so the potential at earth'sEarth's surface is almost zero.So So for all practical purposes we assume its potential to be zero.The The potential at infinity is assumed to be absolutely zero whereas that on earth'sEarth's surface almost zero. If we assume potential at infinity to be zero and earth to be spherical then the potential at the surface of the earth is given by $$\frac{kq}{r}$$,,where $$k$$ is a constant  ,$$q$$ is the charge on earth and $$r$$ its radius.As $$q$$ is extremely small and $$r$$ very large, so the potential at earth's surface is almost zero.So for all practical purposes we assume its potential to be zero.The potential at infinity is assumed to be absolutely zero whereas that on earth's surface almost zero. If we assume potential at infinity to be zero and Earth to be spherical then the potential at the surface of the earth is given by $${kq}/{r}$$, where $$k$$ is a constant,  $$q$$ is the charge on earth and $$r$$ its radius. As $$q$$ is extremely small and $$r$$ very large, the potential at Earth's surface is almost zero. So for all practical purposes we assume its potential to be zero. The potential at infinity is assumed to be absolutely zero whereas that on Earth's surface almost zero. 2 improved formatting; edit approved May 18 '15 at 17:54 AV23 2,81066 silver badges1717 bronze badges If we assume potential at infinity to be zero and earth to be spherical then the potential at the surface of the earth is given by kq/r$$\frac{kq}{r}$$,,where k$$k$$ is a constant ,q$$q$$ is the charge on earth and r$$r$$ its radius.As q$$q$$ is extremely small and r$$r$$ very large, so the potential at earth's surface is almost zero.So for all practical purposes we assume its potential to be zero.The potential at infinity is assumed to be absolutely zero whereas that on earth's surface almost zero. Sanjay Bisht If we assume potential at infinity to be zero and earth to be spherical then the potential at the surface of the earth is given by kq/r,,where k is a constant ,q is the charge on earth and r its radius.As q is extremely small and r very large, so the potential at earth's surface is almost zero.So for all practical purposes we assume its potential to be zero.The potential at infinity is assumed to be absolutely zero whereas that on earth's surface almost zero. Sanjay Bisht If we assume potential at infinity to be zero and earth to be spherical then the potential at the surface of the earth is given by $$\frac{kq}{r}$$,,where $$k$$ is a constant ,$$q$$ is the charge on earth and $$r$$ its radius.As $$q$$ is extremely small and $$r$$ very large, so the potential at earth's surface is almost zero.So for all practical purposes we assume its potential to be zero.The potential at infinity is assumed to be absolutely zero whereas that on earth's surface almost zero. 1 answered May 18 '15 at 17:18 Sanjay Bisht 3111 bronze badge If we assume potential at infinity to be zero and earth to be spherical then the potential at the surface of the earth is given by kq/r,,where k is a constant ,q is the charge on earth and r its radius.As q is extremely small and r very large, so the potential at earth's surface is almost zero.So for all practical purposes we assume its potential to be zero.The potential at infinity is assumed to be absolutely zero whereas that on earth's surface almost zero. Sanjay Bisht


text:
# MEASUREMENTS ON THE FAR WINGS OF AMMONIA LINES BROADENED BY HYDROGEN

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/15905

Files Size Format View
1973-B-13.jpg 109.5Kb JPEG image

 Title: MEASUREMENTS ON THE FAR WINGS OF AMMONIA LINES BROADENED BY HYDROGEN Creators: Varanasi, P.; Pugh, Larry A. Issue Date: 1973 Publisher: Ohio State University Abstract: Absorption due to ammonia lines broadened by hydrogen has been measured between $2200 cm^{-1}$ and $2000 cm^{-1}$. The observed absorption appears to be predominantly due to the far wings of lines in the vibration-rotation bands of ammonia near 3 a, 6 a and 10 a. The shapes of the far wings of ammonia lines collision-broadened by hydrogen are derived. Description: Author Institution: Department of Mechanics, State University of New York, Stony Brook This research was supported by NASA under Grant No. NGR-33-015-139. URI: http://hdl.handle.net/1811/15905 Other Identifiers: 1973-B-13


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# Optimal approximation of nonlinear probability density function by piecewise constant density

Given a nonlinear probability density function F, the problem is to estimate F using histogram over a partition with N intervals.

I have tried to realise this with MATLAB function fmincon, but it seems to always generate local minimum. The optimisation function is the minimisation of the difference between F and the estimated result. As can be seen from the following figure, the estimation cannot be accepted.

How can the optimal result be obtained?


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# Is it possible to ensure security with zero pre-shared information?

Is it possible to secure a communications channel against both passive (sniffing) and active (injecting / MitM) attackers without either legitimate party knowing any pre-shared information?

I know that this isn't possible using "traditional" asymmetric crypto, since an active attacker could create its own public keys and relay the information on both sides. A trusted third party implies pre-shared information, since at least one party must provide their public key to the third party.

Are there any schemes that make this viable, or is it completely impossible?

Update: By "zero information", I mean other than the "address" of the other person, e.g. their computer's IP address, or even their mailing address.

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It's obviously impossible. You need to know at least something. For example you could have the public key double as address. –  CodesInChaos Jul 16 '12 at 9:44
Is IBE (where there's a third party that provides to each party the system parameters and the private key corresponding to that party's address, but no one need give a public key to a third party) also out of bounds? –  poncho Jul 16 '12 at 12:47
@poncho The only thing the two parties have pre-shared is their locations, e.g. an IP address. –  Polynomial Jul 16 '12 at 12:49

Yes. Simply send the data in the clear.

Passive attacks are not possible. For a passive attack to work, the data must be intercepted by someone other than the intended recipient. But by your definition of "pre-shared information" the existence of an intended recipient would count as "pre-shared information" (since both sides would know this). So anyone who receives the traffic is just as much the recipient as anyone else.

Active attacks are not possible. Active attacks involve someone other than the person the other side expects to be sending the data to be able to influence the data or receive the data. Since neither side has any expectations as to who is originating or receiving the data (such an expectation would be "pre-shared information" since both sides would need to have it), such an attack cannot, by definition, exist.

The idea of a "secure channel" to nobody in particular simply isn't coherent. And if both sides knew who they wanted to speak to or hear from, that would be "pre-shared information" by your expansive definition.

So this is not a coherent thing to want.

Consider two people considering such a scheme, Alice and Bill. If Bill knows who Bill is, Alice cannot know who Bill is as that would be pre-shared information. If Alice knows who Alice is, then Bill cannot know who Alice is, as that would be pre-shared information. Thus Bill could not distinguish a secure link to Alice from a secure link to Fred. To Bill, either is just as good. So it matters not if Fred intercepts or distorts the data. Fred is no less the intended recipient.

Update: If literally all you know is the address, then nothing could provide any more security than simply sending to that address. Since the address is all you know, whoever can receive something sent to that address is the intended recipient, right? And it doesn't matter what that person receives, since you are no different from an attacker, they wouldn't care whether they received what you sent or what someone else sent -- they don't know who you are.

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Certificate authorities, as I mentioned, count as pre-shared information. They have to give their certificate to a trusted third party. –  Polynomial Jul 16 '12 at 8:35
Ahh, okay, I'll fix my answer. –  David Schwartz Jul 16 '12 at 8:37
I think your edit went too far the other way. Alice knows Bob, Bob knows Alice, let's say by IP address on a LAN. I'm not sure whether you misunderstood me, or if you're just being pedantic with the aim of making a point. –  Polynomial Jul 16 '12 at 8:48
If all Bob knows is Alice's IP address, then the best Bob can do is communicate with that IP address. Whoever gets it is the intended recipient, since that person meets the only criterion Bob knows or cares about. (Unless you're asking a totally different question like "Can someone prove they are 'entitled' to a particular IP address?" If that's the case, you should ask a more specific question.) –  David Schwartz Jul 16 '12 at 9:23

No. Consider using encryption to protect against a passive adversary. In this case, encryption needs to hold from the sender to the receiver. The sender can verify that the message leaves them encrypted but they have no guarantee that it is not decrypted before the receiver unless if they can authenticate the receiver. Authentication requires knowledge of some secret which would constitute preshared information in your definition.

The closest I believe you could come to a secure channel in this setting would be what is called Secure Message Transmission Protocols. The basic idea is that the sender would split up the message into shares (say 10 shares) such that some threshold (7 shares) are required to reconstruct the message. The sender would send the 10 shares over different channels. This is not secure against an adversary that is one all channels (which your question implies, which is why the answer is still likely "no") but if the adversary is on 6 or less, you get passive security. Active security is possible but the adversary is bounded to less than a third of the channels (byzantine agreement). Anyways, you could also argue that knowing the algorithm to reconstruct the message from the shares is pre-shared information (although not a secret).

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Yes, one needs a manual channel. $\:$ That is, some channel which allows
the parties to compare a short string held by each of them for equality.

www.wisdom.weizmann.ac.il/~naor/COURSE/fc0607_lect7.ppt

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You should post a summary of your source. Your post is utterly useless without the linked material. –  CodesInChaos Jul 16 '12 at 9:53
I'll concede that it wasn't very helpful without the linked material, but I say it was far from "utterly useless" without the linked material. $\:$ It provided the term "manual channel", which is the term that's needed to look up further information on this subject. $\;\;$ –  Ricky Demer Jul 16 '12 at 10:01
I have to agree with @CodeInChaos here. I don't even have software installed to read PPT files. –  Polynomial Jul 16 '12 at 12:49
@RickyDemer.. ok, but that's just being overly picky on his words... –  Pacerier Apr 4 at 23:50


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# Eigenvectors in Matlab/Octave, function “eig()”, why are the eigenvectors output like that? [closed]

You can calculate eigenvectors of a matrix with eig() function like this:

[eigenvectors, eigenvalues] = eig (matrix)

But I can't manage to understand why the eigenvector output is in some kind of unitary module format.

Example:

Matrix: $$\left(\begin{matrix} 2 & -4\\ -1 & -1\end{matrix}\right)$$

Eigenvalues output of the function: $$\left(\begin{matrix} 3 & 0\\ 0& -2\end{matrix}\right)$$

(I get it, -2 and 3 are the eigenvalues, they are in the main diagonal)

Eigenvectors output of the function: $$\left(\begin{matrix} 0.97014& 0.70711\\ -0.24254 & 0.70711\end{matrix}\right)$$ Why those values instead of the eigenvectors?: $$\left(\begin{matrix} -4\\ 1\end{matrix}\right)$$ and

$$\left(\begin{matrix} 1\\ 1\end{matrix}\right)$$

## closed as off-topic by Lord_Farin, Bill Dubuque, PhoemueX, user7530, SemiclassicalFeb 4 '15 at 23:07

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is not about mathematics, within the scope defined in the help center." – Lord_Farin, Bill Dubuque, PhoemueX, user7530, Semiclassical
If this question can be reworded to fit the rules in the help center, please edit the question.

• If you want eigenvectors more along the lines of how a human would calculate them, you can try using symbolic math in Matlab: A=sym([2 -4;-1 -1]) [V,D]=eig(A). This uses sym/eig (documentation). – horchler Feb 4 '15 at 21:22
• It seems Octave sym function has a different syntax, I downloaded the symbolic package but I get an error when trying to insert the matrix: warning: range error for conversion to character value warning: implicit conversion from matrix to sq_string – user213028 Feb 4 '15 at 21:54
• Octave's symbolic math is well behind Matlab's. It may not support matrices. Or you may need to specify the matrix as a string, i.e., A=sym('[4,1;-1,-1]'), which is generally deprecated syntax in Matlab. In any case I recommend that you read Octave's documentation. – horchler Feb 5 '15 at 1:10
• Also, while your question relates to Matlab programming, I think you have a case for asking that it be reopened. The accepted answer makes this clear. – horchler Feb 5 '15 at 1:12

Eigenvectors are determined only up to a scaling by a constant multiplier. So for an eigenvector $(1,1)$, the vectors $(2,2)$ and $(0.5,0.5)$ are the same eigenvector. It looks like Matlab chooses to normalize the eigenvectors to unit norm. This normalization is the most commonly used.
• For that, you might be more interested in using Mathematica. For exactly represented matrices (integer or symbolic entries), it will return eigenvalues and eigenvectors in exact representations whenever possible. In this case, it usually normalizes one entry of the vector to 1, so it would return $(1,1)$ and $(-4,1)$, but possibly $(1,-\frac{1}{4})$. – Victor Liu Feb 4 '15 at 22:08


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# Setting up Apache Tomcat in Cygwin

I'm trying to set up Apache Tomcat on Cygwin and when I run the configtest.sh script, I get this error. My environment variables all appear to be correct, but when java complains about not finding classes, it tries looking in some weird paths like it's starting from the current directory:

``````Using CATALINA_BASE:   C:\cygwin\usr\local\apache-tomcat-7.0.26
Using CATALINA_HOME:   C:\cygwin\usr\local\apache-tomcat-7.0.26
Using CATALINA_TMPDIR: C:\cygwin\usr\local\apache-tomcat-7.0.26\temp
Using JRE_HOME:        C:\Program Files (x86)\Java\jre7
Using CLASSPATH:       C:\cygwin\usr\local\apache-tomcat-7.0.26\bin\bootstrap.jar;C:\cygwin\usr\local\apache-tomcat-7.0.26\bin\tomcat-juli.jar
Exception in thread "main" java.lang.NoClassDefFoundError: org/apache/catalina/startup/Bootstrap
<<No stacktrace available>>
file:/usr/local/apache-tomcat-7.0.26/bin/C,
file:/usr/local/apache-tomcat-7.0.26/bin/\cygwin\usr\local\apache-tomcat-7.0.26\bin\bootstrap.jar;C,
file:/usr/local/apache-tomcat-7.0.26/bin/\cygwin\usr\local\apache-tomcat-7.0.26\bin\tomcat-juli.jar], parent=null}
Configuration error detected!
``````

Can anyone tell me what I'm doing wrong?

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You're trying to mix Windows and Cygwin paths. –  Jim Garrison Feb 28 '12 at 20:29
my paths should be getting passed to java as Windows paths though. That's what the startup script does. So I don't know why they show up all funky in the stack trace. –  John Peter Thompson Garcés Feb 28 '12 at 20:46
Actually, I see the problem. It's that \$_RUNJAVA calls /usr/bin/java instead of my windows jre installation. I don't know what to do about this though. –  John Peter Thompson Garcés Feb 28 '12 at 21:21
There's a couple different solutions here: stackoverflow.com/questions/6913894/… –  Costa Feb 28 '12 at 21:28
I fixed it. I was being an idiot and not realizing that I was setting my JRE_HOME variable after _RUNJAVA gets set with the default value. –  John Peter Thompson Garcés Feb 28 '12 at 21:40

The file URLs shown in the stacktrace don't look correct. The classpath looks like it was split by the unix path separator, not the windows one, and the slashes are windows slashes, not unix ones.

``````file:/usr/local/apache-tomcat-7.0.26/bin/C,
file:/usr/local/apache-tomcat-7.0.26/bin/\cygwin\usr\local\apache-tomcat-7.0.26\bin\bootstrap.jar;C,
file:/usr/local/apache-tomcat-7.0.26/bin/\cygwin\usr\local\apache-tomcat-7.0.26\bin\tomcat-juli.jar
``````

If I were you, I'd try to set any path related environment variables in cygwin rather than rely on windows, since you are running a bash script. You can make the cygwin value dependent on the windows variables by using the cygpath program:

``````export CLASSPATH=`cygpath \$CLASSPATH`
``````
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the startup script does this: `CLASSPATH=`cygpath --path --windows "\$CLASSPATH"` ` before passing the path to java –  John Peter Thompson Garcés Feb 28 '12 at 20:56
isn't that ^ supposed to work correctly? –  John Peter Thompson Garcés Feb 28 '12 at 21:02
--windows prints the windows version of the path. I'd be surprise –  Pleepleus Feb 29 '12 at 1:27
yeah, cygpath was working correctly, but I figured out that _RUNJAVA in the startup script was calling my cygwin port of java rather than my windows installation. So it was passing a windows version path to a linux program. I changed the startup script so that _RUNJAVA points to my windows installation of java, and everything works fine now. –  John Peter Thompson Garcés Feb 29 '12 at 14:42