Why I get negative values on using periodogram after Fourier analysis?

sorry for bothering you with this question today. I am trying to analyze wave data that was produced using a wave tank. The period used for the waves is 1.7s, the waves encountered an obstacle at some point and then reflections are expected.

I plotted one of the sensors that are a wave gauge system. And I obtained the next plot:

Imaage of wave amplitude vs time

The x is the time in seconds and the y the wave height in mm. After this I use the code:

ListLinePlot[Abs[Fourier[datcy]], PlotRange -> All] 

And then I get the Fourier transform and I also plot just the data:

Fourier transform of the data data plotted

I know the plot is reflected and that is why I have a double one, but what I don’t get in wolfram or maybe on signal analysis is how I get a power spectrum that is negative after this:

Periodogram[datcy[[All, 2]], Frame -> True,  

GridLinesStyle -> Directive[Red, Dashed], PlotRange -> All]

Power spectrum

It’s on DB?, if that is true then technically there are no negative values and I should interpret as a -150 DB?. I am a bit lost here. Also, have a bit of doubt about why the amplitude of the Fourier plot doest not relate to the amplitude of my wave?.

Doubts in some inequalities used in asymptotic analysis

I was going through this recent paper, and I had a couple of doubts in the final analysis of complexity of the scheme (you don’t need to go through the whole paper). I included three questions here, as I thought they seem to simple questions.

  1. In Pg 17 (last four lines, see after equation 7), there is this inequality that is used (here, $ k(n) = \sqrt{\frac{n\delta(n)}{\log n}}$ and $ \delta(n) = o(n / \log n)$ ):

$ \frac{\binom{n}{a}}{\binom{^n/_k}{^a/_k}^k} \leq (^n/_k)^k$

Can I know a proof for it?

  1. Similarly, in the beginning of Pg 18, how is this possible? (the above inequality is used to get here though, $ (n / k)^{k / 2}$ thing, and don’t worry about the meaning of $ \mathtt{ss}$ )

$ \mathtt{ss} \leq \sqrt{\binom{n}{\frac{n}{2}-\delta(n)}}\cdot (n / k)^{k / 2} \cdot \binom{k}{2\delta(n)} \cdot 2^{(2\delta(n)+1)n / k} \leq 2^{n / 2 + o(n)}$

  1. Also, this one might be a bit trivial, in Pg 17, one inequality above equation 7, the $ O(n)$ term is dropped, isn’t that relevant?

What is “software development analysis”? [on hold]

I was reading a description about a bioinformatics course and it say that it has an emphasis on “software development analysis”. I tried googling the phrase “software development analysis” but I cannot find a definition. Does it mean analysis of software development or is it an actual subject area in software development? Please forgive me I am new to software development.

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What is “rule-based” analysis in malware detection?

I’ve read a few articles that describe the heuristic detection used by AVs as being either “weight-based” or “rule-based”. The weight-based aspect seems to make sense, but I don’t understand what “rule-based” detection is or how it works.

This article describes rule-based detection as follows:

Nearly all nowadays utilized heuristic approaches implement rule-based systems. This means, that the component of the heuristic engine that conducts the analysis (the analyser) extracts certain rules from a file and this rules will be compared against a set of rule for malicious code. If there matches a rule, an alarm can be triggered.

I just don’t understand what a “rule” is in this context. How is it different from any other signature. If it is one of the many characteristics that may be used in weight-based detection, how is this approach significantly different than that?

As is analysis of legacy systems

I’ve been tasked with performing an ‘as is’ analysis of a monolithic legacy system in my organisation. I’ve been conducting interviews with the technical team responsible for developing the system along with other techniques (such as but not limited to, observing people using the system, surveying, meetings etc), and I’ve been creating data flow diagrams to map out the system.

As I’ve never conducted an ‘as is’ analysis of a legacy system, what is the best way to model the system? I’ve been creating DFDs although I’m begging to question if this is the most appropriate approach.